>1 



' 




THE LIBRARY 

OF 

THE UNIVERSITY 

OF CALIFORNIA 

DAVIS 

GIFT OF 

DONALD 0. EMERSQN 



THE PHYSICS 

OF 



EARTHQUAKE PHENOMENA 



CARGILL GILSTON KNOTT 

D.Sc., F.R.S.E., ETC. 

FOURTH ORDER OF THE RISING SUN, JAPAN 

PROFESSOR OF PHYSICS (1883-91) IN THE IMPERIAL UNIVERSITY OF JAPAN 
LECTURER IN APPLIED MATHEMATICS, UNIVERSITY OF EDINBURGH 



OXFORD 

AT THE CLARENDON PRESS 

1908 
LIBRARY 

UNIVERSITY OF CALIFORNIA 
DAVIS 



HENRY FROWDE, M.A. 

PUBLISHER TO THE UNIVERSITY OF OXFORD 

LONDON, EDINBURGH 
NEW YORK AND TORONTO 



PREFACE 

HAVING been appointed Thomson Lecturer in the United 
Free Church College in Aberdeen during the Session 1905-6, 
I was invited by Principal Iverach to deliver a course of 
lectures on earthquakes. This book is the outcome of 
these lectures, which probably are unique in having been 
the only systematic course ever delivered on the subject in 
this country. 

Since the days when I studied Geology under Sir Archibald 
Geikie, then Professor in Edinburgh University, I had always 
retained a strong interest in the many physical problems 
suggested by geological and geographical facts. Accord- 
ingly when, in 1883, I entered on my duties as Professor of 
Physics in the University of Tokyo, Japan, my interest in 
seismological questions naturally received a great impetus. 
With Professor John Milne as a colleague it was impossible 
for me to escape being to some extent fired by his enthu- 
siasm. A glance through the succeeding pages will show 
how largely this eminent seismologist has influenced the 
thoughts which find expression. It was my good fortune 
to witness the conception and growth of many of his most 
fruitful ideas, to see how at every turn he appealed to 
experiment to elucidate a new problem in seismology, and 
to note the persistent ingenuity with which he followed up 
an almost invisible line of research. 

Between 1880 and 1890 Seismology as a distinct branch 
of science was in the making, not merely in Japan, but in 



iv PREFACE 

Japan for the whole world. The sharp earthquake of 
February 22, 1880, which did a considerable amount of 
damage in Yokohama and Tokyo, had one important scien- 
tific consequence. It led to the realization of an idea which 
had for some time been hovering in the minds of Professors 
Milne, Chaplin, Ewing and others, namely, the establishing 
of a society for the study of earthquake phenomena, to be 
called the Seismological Society of Japan. With a member- 
ship of over one hundred, of whom about one-third were 
Japanese of position and influence in educational circles, this 
Society entered upon a brief but vigorous life of twelve years' 
duration. The papers read at its meetings and published 
in its Transactions did more to give shape to the modern 
science of seismology than the work of any other institution 
or combination of institutions the wide world over. The 
most conspicuous of this truly cosmopolitan band of enthu- 
siasts was unquestionably Professor Milne, who, in addition 
to enriching the Transactions by his numerous and pregnant 
contributions, sent annually to the British Association a 
report containing the cream of the lively discussions and 
valuable work done by the members of the Society. 

One of my aims has been to show what a remarkable 
lead the Seismological Society of Japan took, not only in 
following up the problems originally associated with the 
names of Mallet, Hopkins, and Perrey, but in striking out 
on quite new paths. Having done its pioneer work the 
Society came to a natural end in 1892. The study of 
seismology had then become of national importance, and 
was receiving strong support from the Imperial funds under 
the enlightened rule of the Emperor of Japan. 

During the existence of the Seismological Society sixteen 
volumes of Transactions were published ; but the publica- 
tion was continued by Professor Milne till 1895 under the 



PREFACE v 

title of the Seismological Journal of Japan, the four volumes 
of which were regarded as corresponding to volumes XVII 
to XX of the Society's Transactions. Complete sets of 
these important publications are difficult to obtain, many 
copies having been destroyed in 1895 by a fire which 
practically consumed Professor Milne's own precious library 
of seismological literature. 

In no respect do I consider this book to be a complete 
account of earthquake phenomena. For these the reader 
must refer to Professor Milne's own publications Earthquakes 
and Seismology ; or to Montessus de Ballore's large volumes 
Les Tremblements de Terre and La Science Seismologique. 
I have purposely limited my discussion to those phenomena 
which have suggested physical investigations, or which from 
their nature touch closely on physical theory. In short, 
I treat the subject not as a branch of technical geology, 
but as belonging to the wider domain of natural philosophy, 
both experimental and mathematical. Consequently there 
are important aspects of seismology which are passed over 
in silence or are referred to only incidentally. 

I have culled largely from the writings of recent investiga- 
tors, reproducing in many cases their diagrams and illustra- 
tions. Some of these diagrams have been considerably re- 
duced, so as to obviate the necessity of using folding plates. 
In no case, however, so far as I am aware, have the broad 
features of the diagrams under consideration been obliter- 
ated. While thanking all from whom I have benefited in 
this way, I would specially record my indebtedness to Prince 
Galitzin, Professor Milne, Mr. Oldham, Captain Dutton, 
Dr. Davison, Mr. Middlemiss, Mr. Heath, the Directors of 
the Coats' Observatory (Paisley), and last, but not least, to 
my former pupil, Professor Omori, of the Imperial University 
of Tokyo. Although differing from the Japanese seismo- 

a 3 



vi PREFACE 

legist on several points, I appreciate and admire to the full 
his zeal and skill in handling the ever-accumulating statistics 
and in analysing the intricate records of earthquakes. 

During the printing of the book new and better data 
have come to hand, and important improvements have been 
effected in the construction of recording apparatus. It was 
impossible under the circumstances to take account of all 
of these. The broad principles of the construction and action 
of seismographs remain the same ; but, as in every other 
branch of science, improvements must come. All honour 
to him through whom they do come. In particular, Pro- 
fessor Wiechert, of Gottingen, has in recent years effected 
notable developments ; and in Professor Marvin, of Wash- 
ington, we have the promise of a seismologist of singular 
clearness of vision. 

CARGILL GILSTON KNOTT. 



UNIVERSITY OF EDINBURGH, 
August, 1908. 



TABLE OF CONTENTS 

.CHAPTER I 

INTRODUCTION PAOB 

Astronomy and Geology. The Folded Rock. Stresses and Strains. 
Bending Yielding Rupture. Flow of Solids Adams and 
Nicolson. The Crust of the Earth. Isostasy. Elastic and 
Quasi-elastic 1 

CHAPTER II 

EARTHQUAKE PHENOMENA 

^immediate and Transient Effects of an Earthquake. -^Earthquake 
Sounds. Stifling Effect of Viscosity. Destructive Effects. 
Undulations. Projection of Stones. ^Buildings, Tombstones, 
Monuments. Vorticity of Ground. ^-Horizontal and Vertical 
Displacements. ^jGohtraction and Expansion of Areas. Cadas- 
tral Surveys 10 

CHAPTER III 

SEISMIC SURVEYS 

Collection of Reports. *-"$cale of Intensities. Isoseisms. Laibach, 
Charleston, Assam. Determination of Epicentre. Coseismal 
Lines. Dutton's Discussion of Time Observations. Deter- 
mination of Depth of Focus. Dynamical Measure of Intensity. 
West's Formula. Milne's and Omori's Experiments. Holden- 
Omori Dynamical Scale of Intensity. Dutton's Method of 
determining Depth of Focus. Davison's Isacoustic Lines. 
Twin Earthquakes. Harboe's Herdlinien .... 26 

CHAPTER IV 
INSTRUMENTAL SEISMOLOGY 

Instrumental Seismology^ Development of Seismographs in Italy 
and Japan. Realization of the Steady Point. Stevenson's 
Aseismic Joint. Vertical Pendulum. Forbes's Inverted 
Pendulum. Ewing's Duplex Pendulum. Horizontal Pendu- 
lum. Bracket Seismograph. Vertical Seismograph. Record 
of Complete Motion. ^.Milne's Horizontal Pendulum. Omori's 
Horizontal Pendulum. Wiechert's Seismographs. Tanaka- 
date's Vertical Seismograph. Trustworthiness of Record . 48 



viii TABLE OF CONTENTS 

CHAPTER V 

SEISMOMETRY PAGM 

Dyn.-miical Theory of the Horizontal Pendulum. Analysis of 
Motions. Tilting and Horizontal Movement inseparable. 
Galitzin's Discussion. Effect of Frictional Resistances. 
Oniori's Writing Lever. Galitzin's Experiments. Galitzin's 
Results. Theory of Forced Vibrations. Distinction between 
Static and Kinetic Sensitiveness. General Conclusions. 
Application to Seismograms. Untrustworthiness of Hori- 
xontal Pendulum Records ....... 66 

CHAPTER VI 
EARTHQUAKE DISTRIBUTION 

Seismic and Aseismic Regions. Definition of Seismicity. Survey 
of Limited Areas. Milne's Survey of Tokyo. Earthquake 
Catalogues. De Ballore's Methods. Rudolph's Analysis of 
Sea-quakes. Milne's Chart of Large Earthquakes. De Bal- 
lore's Criticisms . . . . . . . . .90 

CHAPTER VII 

PERIODICITIES 

Earthquake Frequency. Possible Causes. Tidal Stresses due to Sun 
and Moon. Annual and Semi-annual Periodicities. Method 
of Analysis. Rayleigh and Schuster's Application of Theory 
of Probabilities. Expectancy in Hap-hazard Events. Author's 
Original Investigations. Davison's Corroborative Work. 
Annual Frequency in Northern and Southern Hemisphere. 
Possible Meteorological Causes. Slow Barometric Changes. 
Omori's Discussion of Japan Earthquakes. Criticisms and 
Conclusions. Rainfall, Snowfall, Denudation, Deposition . 101 

CHAPTER VIII 

PERIODICITIES (continued) 

Lunar Periodicities. Lunations. Milne's Catalogue of Japanese 
Earthquakes. Analysed in Terms of Months. Author's 
Analysis. Imamura's Later Work. De Ballore's Analysis. 
Author's Examination of Lunar Day Periodicity. Omori's 
Investigations. Oldham's Discussion of Aftershocks of Assam 
Earthquake. Solar Day Periodicities. Davison's Analysis. 
Omori's Investigation of the Fluctuations in Aftershocks . 130 



TABLE OF CONTENTS ix 

CHAPTER IX 
ELASTICITY 

PA(j!Ili 

Elasticity of Bulk and Form. Rigidity and Incompressibility. Shear 
and Shearing Stress. Extension and Bending. Static and 
Kinetic Moduli. Elastic Constants for Rocks. Milne and 
Gray. Nagaoka and Kusakabe. Adams and Coker. Speed 
of Propagation of Disturbance . . . . . .156 

CHAPTER X 

ELASTIC WAVES 

Reflexion and Refraction of Waves. Two Flexible Ropes of Different 
Weight. Two Elastic Media with a Common Boundary., One 
Type of Wave Motion in Fluids, Condensational. Two Types 
of Wave Motion in Solids, Condensational and Distortional. 
Reflexion and Refraction of Elastic Waves at the Boundary 
of two Media. Rock and Water. Rock and Rock. Rock 
and Air. Water and Air. Earthquake Barriers. Seismic 
Energy largely retained in Crust. Interference Phenomena. 
Viscosity. Wave Groups 171 

CHAPTER XI 
UNFELT SHAKINGS OF EARTH 

Minute Movements. Daily Oscillations of the Plumb. Von Rebeur 
Paschwitz. Milne's Theory. Pulsations. Motions due to 
Distant Earthquakes. Comparison of Seismograms. Typical 
Earthquake Record. Preliminary Tremors. Large Waves 
or Principal Portion. Omori's Analysis of Periods. Inter- 
pretation of Record. Resonance frequent . . . .186 

CHAPTER XII 

SEISMIC RADIATIONS 

Identification of Phase. Relation between Period and Amplitude. 
Selected Data of Kangra Earthquake (1905). Decay of Inten- 
sity with Distance. Early Tremors killed out. Milne's 
Method of Fixing Origins. Omori's and Laska's Modifications. 
Milne's World-shaking Earthquakes. Milne's and Oldham's 
Time Graphs. Imamura's Statistical Discussion. The Guate- 
mala Earthquake (1902). Oldham's Speculations. General 
Comparison of Times of Transit. Arcual Transmission of 
Large Waves. Approximate Chordal Transmission of Tremors. 



x TABLE OF CONTENTS 

I'.UJE 

Fisher's Hypothesis of Two Waves in Liquid Interior. Evi- 
dence as to Longitudinal and Transverse Vibrations. Naga- 
oka's Stratum of Maximum Velocity. Angles of Emergence 
measured by Schliiter. Brachistochronic Paths : Kove- 
sligethy, Rudzki, Knott, Benndorf. Mathematical Theory 
compared with Observation. Poisson's Ratio satisfied. 
Energy Distribution. Group Velocities. Anomalous Disper- 
sion (Nagaoka). Lamb's Vibration of Elastic Sphere. Jeans, 
Rayleigh, and Love on Stability of the Earth . . .210 

CHAPTER XIII 

MISCELLANEOUS RELATIONS 

Miscellaneous Relations. Building Construction. Vibration of 
Locomotives. Vibration of Bridges. Suboceanic Changes. 
Destruction of Telegraph Cables. Milne's Comparison of 
Earthquake Frequency and Movements of the Earth's Pole : 
Newcomb, Hough. Albrecht's Curves. Discussion of the 
Relation. Terrestrial Magnetism and Seismicity. Earth- 
quakes and Volcanoes. See's Theory of Steam Explosions. 
Murray's Views of Elevation of Continents. Internal con- 
dition of the Earth : Fisher, Chamberlin. Evolution of the 
Earth. Jeans and Sollas . 259 

INDEX 279 



ILLUSTRATIONS 

FlG. PAGE 

1. Elastic Hysteresis in Rocks 15 

2. Inglis's Monument at Chhatak .... To face p. 19 

3. Monument and Pillars in Elevation and Plan ... 20 

4. Willan's Memorial, Shillong ....... 22 

5. Triangulation after Shock .24 

6. Isoseisms of Charleston Earthquake . . . , . 28 

7. Isoseisms of Assam Earthquake . . . . . . 29. 

8. West's Formula . . 37 

9. Intensity Curve, after Dutton 40 

10. Isoseisms and Isacoustics of Hereford Earthquake ... 43 

11. Isoseisms of Kangra Earthquake ...... 45 

12. Duplex Pendulum 54 

13. Theory of Steady Point 56 

14. Theory of Vertical Motion Seismometer 59 

15. Complete Earthquake Record 60 

16. Milne's Horizontal Pendulum 62 

17. Omori's Horizontal Pendulum 64 

18. Theory of Horizontal Pendulum . 67 

19. Connexions of Omori's Writing Lever 70 

20. Galitzin's Horizontal Pendulum Tracings .... 72 

21. Galitzin's Horizontal Pendulum Tracings . . . .73 

22. Galitzin's Horizontal Pendulum Tracings .... 74 

23. Resonance in Forced Vibrations 80 

24. Seismograms of Felt Earthquakes 86 

25. Seismograms of Felt Earthquakes 88 

26. Milne's Chart of Earthquake Districts 97 

27. Annual and Semi-annual Periodicities 118 

28. Lunar Periodicities 132 

29. Shear and Shearing Stress 158 

30. Waves along Slack Ropes . .171 

31. Reflexion and Refraction of Waves 177 

32. Reflexion and Refraction of Waves . .... 182 

33. Diurnal Oscillations of Level 189 



xii ILLUSTRATIONS 

FlO. PAGE 

34. Pulsations of the Ground 192 

35. Records of Felt Earthquakes in Tokyo 195 

36. Omen's Records of Ceram and New Guinea Earthquakes . 197 

37. Omori's Typical Earthquake Record 200 

38. Records of Kangra and San Francisco Earthquakes . .201 

39. Edinburgh Records of Several Earthquakes . . To face p. 205 

40. Various Records of Kangra Earthquake ... ,, 215 

41. Paisley Records of Various Earthquakes . . 217 

42. Milne's Time-Curves 224 

43. Seismic Radiations through the Earth 252 

44. Albrecht's Motion of the Earth's Pole 2f>3 



CHAPTER I 

INTRODUCTION 

Astronomy and Geology. The Folded Rock. Stresses and Strains. Bend- 
ing Yielding Rupture. Flow of Solids Adams and Nicolson. The 
Crust of the Earth. Isostasy. Elastic and Quasi-elastic. 

IT is worthy of remark that the oldest science is Astronomy 
and the youngest Geology. Ages before any systematic 
attempt had been made to unravel the complexities of the 
structure of the earth on which we live, the human mind 
had grasped the scientific unity of the Cosmos. 

The reason of this is not far to seek. It lies in the apparent 
simplicity of the celestial problem, which early disclosed 
itself to the gropings after knowledge of the ancient Chal- 
deans, Akkadians, and Indians. 

The foundation was laid by the astrologer, who from the 
ordered movements of the heavenly host would fain read the 
hidden scroll of futurity. Impelled by the eager chase after 
things occult, the mind of civilized man gradually accumu- 
lated a mass of knowledge, the mere knowing of which 
became in time its own reward. 

The early crystallization of this mass of knowledge into 
a body of scientific truth depended in large measure upon the 
comparative simplicity of the problem of the solar system. 
The modern astronomer, aided by his instruments of re- 
search, knows of complexities in the heavens far surpassing 
anything presented by our own system of sun and planets. 
If, instead of having one great central orb greatly exceeding 
in mass all the planets and satellites combined, we had been 
blessed with what is known as a double star system, then 
truly would the ancient astronomers have been sorely tried 
in their efforts to reduce the motions of suns and planets to 
combinations of cycles. In the face of such a stupendous 
problem the mathematical powers of our race might possibly 
have developed more rapidly than has been the case. But 
it is infinitely more probable that, with two suns instead of 

KNOTT B 



2 EARTHQUAKE PHENOMENA I 

one influencing the motion of our earth, man would have 
been content to accept the facts without making any effort 
to find a formula to co-ordinate them. The very complexity 
of the problem would have led to its neglect ; and so has 
it been with geology. 

To form a theory of astronomical phenomena needed 
only a certain basis of geometry and arithmetic. Guided 
by the broad and therefore simple facts of experience, man 
soon recognized a rhythm in celestial motions, and by 
ingenious use of the geometry of the circle was able to 
express this rhythm quantitatively with an accuracy suffi- 
cient for his wants. But in the chaos of rocks and hills, in 
the apparently lawless recurrence of earthquakes and storms, 
he found no guiding line. 

Even after the Newtonian system of worlds had been 
established as the first great scientific generalization, man's 
knowledge of his own planet remained practically nil. Some 
adventurous minds had speculated on the causes of earth- 
quakes and volcanoes, and even on the interior constitution 
of the earth. But not till the nineteenth century did geology 
as a science begin to take form. 

Looking back from the scientific height now gained, we 
easily see why geology should be among the most recent of 
sciences. It requires for its true development a sound 
knowledge of physical principles, chemical facts, and anatom- 
ical structure. For instance, how can we hope to read the 
page of the folded rock unless we know to some extent the 
effects of heat and of stress and strain upon heterogeneous 
material. 

A folded rock. The very words suggest a past suggest 
a first state of unfoldedness, a simple stretch of pebble and 
sand laid down along the edge of a continent or island by 
the never-ceasing action of running water and the ebb and 
flow of tide. The ocean rises or the land sinks ; and the 
sandy, pebbly stretch becomes covered with newer sediment, 
and finally, by pressure and cohesion, it is consolidated into 
a rock. Sandwiched in between layers of older and of 
newer age, this particular stratum enters upon a life history 
of extraordinary vicissitudes. It is bent, doubled, folded, 



I INTRODUCTION 3 

drawn out, snapped across, and tortured in all kinds of 
ways ; and yet, through all, it retains the memory of its 
birth it remains a stratified rock. Possibly through the 
influence of heat or pressure it may have lost its more 
obvious stratified character or assumed a false stratification ; 
but its origin is clear as noonday to the experienced eye of 
the geologist. 

Moreover, it is because of its stratified character that we 
know it to have been the victim of these varied strains of 
bending, doubling, and folding. Had the solid crust of our 
earth been isotropic, having equal properties in all direc- 
tions, we should never have been able to recognize those 
foldings and bendings of rock, or to infer the existence of 
the enormous pressures, pulls and thrusts, which must have 
accompanied, and in a sense, produced the strains. But by 
the very mode of its formation under the combined influ- 
ence of hydrodynamic and gravitational forces our stratified 
rock is aeolo tropic, and preserves its characteristic aeolo- 
tropy through aeons of change. Thus the pure surface 
action of air and water is an indispensable factor in enabling 
us to determine the so-called hypogenic forces which also 
help in the process of earth sculpture. 

There are other factors, such as volcanoes and geysers, 
whose evidence is very direct as to the igneous or. plutonic 
character of the hidden places of the earth. It requires no 
technical knowledge of physical principles to infer from 
such phenomena that the interior of the earth is at a high 
temperature. But it is quite otherwise when we come to 
consider the scientific evidence based on the convolutions 
and fractures of stratified or sedimentary rocks like con- 
glomerates, sandstones, and shales. From the date of their 
deposition in horizontal or nearly horizontal layers, along 
the margins of seas or lakes, they have passed through 
a varied experience. They have sunk to form the floor of 
lakes and seas, and have then been raised into plateaux and 
mountain masses. This process of alternate upheaval 
and subsidence may have been repeated many times, slowly 
no doubt, but none the less surely. And just as an ocean 
swell in its majestic motion means at every point a rise and 

B 2 



4 EARTHQUAKE PHENOMENA I 

fall, and over each bit of surface a curving and an uncurving,. 
eo has it been with the see-saw motion of the earth's rocky 
crust. Slow but irresistible, with prolonged pauses, these 
movements of the crust as demonstrated by the succession 
of strata were of necessity accompanied by flexure of rock 
stretches originally flat. We can, in the geological record r 
find examples of all kinds of flexure, from a single slight 
convexity or concavity to great synclinal and anticlinal folds, 
such as constitute the Jura mountains, the Carpathians, or 
the Appalachians. 

Let us consider for a moment the nature of the system 
of forces which might be imagined as giving rise to this 
condition of things. If we assume that the strata have not 
been appreciably extended along the direction of their 
original stretch, then we must admit a great pressure com- 
pressing their whole length into a distance smaller than the 
original length. The source of this tangential pressure has 
generally been referred to the contraction of the earth as it 
cooled. Experiments by Favre, Daubree, Mellard Reade, 
Willis, Cadell, and others, on the effects of lateral crushing 
on the form of layers of wax or clay have certainly gone far 
to prove the sufficiency of this explanation. Some may at 
first find it difficult to imagine how a solid stratum of sand- 
stone can yield by bending and not be ruptured in the 
process. But it has been established experimentally that 
a solid will flow like a very sluggish liquid when a suitable 
combination of forces acts upon it. 

Of the many interesting experiments bearing on this 
subject, perhaps the most important from our present point 
of view are those conducted by Professor F. D. Adams and 
Dr. J. T. Nicolson on the flow of marble. 1 

Small columns of pure Carrara marble were surrounded 
by close fitting iron tubes and then subjected to end pres- 
sures. When the pressure reached about 18,000 Ib. to the 
square inch the tube surrounding the marble began to bulge, 
and on removal of the pressure the marble was found to be 
permanently distorted. The deformed marble was firm and 

1 Philosophical Transactions, vol. cxcv, A, 1901 ; or Proceedings of the 
Royal Society, vol. Ixvii, 1900. 



I INTRODUCTION 5 

compact, but it could be distinguished at once from the 
original unstrained rock by its turbid appearance. Micro- 
scopic examination showed that the material had broken 
down along certain lines of shearing, the granulated minutely 
broken structure being what is known as cataclastic. In 
this condition the rock was found to have become markedly 
weaker than at first. When, however, the same treatment 
was given to the material at a high temperature of 300 and 
400 C., no cataclastic structure could be detected, and the 
resistance to crushing had not appreciably diminished. In 
this case there was no breaking down, and the whole move- 
ment was due to the changes in the shape of the component 
calcite crystals. 

Thus under suitable stresses cold rock can be permanently 
strained, becoming moulded to new forms by breaking up 
along the lines of greatest tangential stress, but yet without 
disintegration. The rock becomes less resistant during the 
process, and subsequent straining is more easily effected. 

Bearing these facts in mind, we may imagine the bending 
and folding of strata to take place in the following manner. 
The strata will begin to yield where the appropriate com- 
binations of pressure and tension are most developed. As 
soon as a particular part has yielded sufficiently there will 
be relief of stress, and the yielding will cease. The condition 
of stress favourable to further yielding will probably be 
developed somewhere else along the stratum, which may in 
this way become gradually bent and folded more or less 
along its whole length. 

If during this process fracture occurs, immediately an 
earthquake shock will be transmitted through the neighbour- 
ing material. If the fracture be accompanied by a relative 
displacement of the fractured faces in other words, if 
a, fault be produced, the rocks in the vicinity will experience 
.a seismic disturbance, which will be transmitted to distances 
varying with the strength of the disturbance. 

Faults or dislocations in the continuity of the strata which 
compose the earth's crust are the rule and not the exception, 
and imply the ceaseless action of powerful pressures and 
tensions in suitable combination. These must result from 



6 EARTHQUAKE PHENOMENA I 

the action of some general terrestrial cause, such as we may 
associate with the cooling and shrinking of the earth. The 
most probable combination of stresses on the assumption of 
a cooling and contracting earth will be tangential or hori- 
zontal pressures with possibly tensions acting vertically. 
The resulting lines of maximum shearing stress will then be 
inclined at angles of 45 to the horizontal ; and in directions 
approximating to these we should expect the yielding to 
take place. This matter is discussed in an interesting 
manner by E. M. Anderson, of the Scottish Geological 
Survey, in a paper on the Dynamics of Faulting. 1 

It is thus abundantly evident that the crust of the earth 
has been subject, and still is subject, to the influence of forces 
and stresses, the ultimate source of which is gravitation 
acting on a heterogeneous mass. 

When using the phrase ' crust of the earth ' we must not 
regard it as being more than a convenient term for the 
superficial layers more or less closely resembling the parts 
which are accessible to direct observation. It is no doubt 
a survival of the crude hypothesis that the earth is molten 
inside and covered with a comparatively thin shell of solid 
matter ; but this hypothesis is no longer tenable. 

So far as it is accessible to us the crust of the earth is 
intensely heterogeneous in its structure ; and we may 
assume a corresponding heterogeneity down to a depth of, 
say, ten to fifty miles. 

Such fairly deep-seated heterogeneity seems to be neces- 
sary when we consider the significance of continental raised 
areas and oceanic deeps. From the highest crests of land 
to the deepest caves of ocean there is a drop of, roughly, 
twelve miles. Were the material which builds the Himalaya 
clump of the same density as that which forms the floor of 
the ocean, a system of stresses would be called into existence 
which would cause a real flow of solid matter from beneath 
the continental dome. We seem rather to be compelled to 
assume that the average density of mountain building rock 
is less than the density of the material which lies beneath 
the ocean waters. In this way a certain average state of 

1 See Transactions of the Edinburgh Geological Society, vol. viii, 1905. 



I INTRODUCTION 7 

equilibrium is preserved in the crust of the earth, a so-called 
isostatic state or state of isostasy. The condition may be 
simply illustrated by means of the hydrostatic experiment 
of the U-tube with mercury in the bend when water is poured 
into the one limb. The water surface in this limb is at 
a much higher level than the mercury surface in the other, 
and yet the conditions of hydrostatic equilibrium are 
satisfied through the mercury substratum. 

It is admitted generally by geologists that continental 
areas have increased, and that seas have deepened during 
the progress of geologic ages. One strong piece of evidence 
in favour of this view is the wider geographical distribution 
of similar animal types the further back we go in geological 
time. If we accept this conclusion, one immediate conse- 
quence is that on the whole the conditions which make for 
upheaval must have over-balanced the conditions which 
make for denudation and waste. The isostatic state is 
therefore never one of complete equilibrium, but only an 
approximation to it. Readjustments are always going on 
as the mountain crests and slopes are worn away ; and it is 
this process of continual readjustment which every now and 
again culminates in a sudden fracture or snap, and generates 
an earthquake. 

The probable location of all earthquakes is therefore in 
the heterogeneous crust. It has been, and still is, the seat of 
extensive changes ; and earthquakes are the necessary 
concomitants. 

Let us suppose, then, that some disturbance takes place 
in the earth's crust a faulting or slip of contiguous rocks, 
a snap or explosion or a cave-in of material anything, in 
fact, which involves a transmission of shock outwards. 
What kinds of motion would be naturally expected ? 

1. With sufficiently intense shock and appropriate com- 
binations of stresses the material might be fractured or 
disintegrated. 

2. With less intensity of shock there might be straining 
which just stopped short of disintegration or fracture, but 
which left a permanent change of configuration of neigh- 
bouring parts. 



8 EARTHQUAKE PHENOMENA I 

3. There might be merely temporary changes of configura- 
tion, from which the material recovered after cessation of the 
shock. 

All these kinds of motion are met with in earthquakes. 
The first class necessarily involves the second and third ; 
and the second involves the third. It is not possible for 
a fracture or rupture to occur without giving rise to displace- 
ments and vibrations of less violent character from those 
which just stop short of breakage down through an infinity 
of gradations to those which are true elastic vibrations. 
The classification given above is not perhaps severely 
scientific no classification ever is ; but it is convenient 
for purposes of discussion. 

There have been, and are, dislocations inrocks intermediate 
in character between the clear rupture and the permanent 
shearing without rupture. Nevertheless, broadly speaking, 
there is a marked distinction between these two kinds of 
strains. As soon as a crack or break occurs the molecular 
conditions are abruptly changed, and the physical problem 
is altered. At the instant of occurrence of the break, 
unbalanced molecular forces come into existence ; and 
these produce in the material on both sides a dynamic shock 
which is transmitted in all directions as an elastic or quasi- 
elastic disturbance. These terms, elastic and quasi-elastic, 
will be found very convenient, and indeed almost necessary, 
when reference has to be made to the kinds of non-rupture 
movements just described. 

Elastic is used in its true physical sense of that property 
in virtue of which a substance resists deforming or com- 
pressing stresses, and recovers its original unstrained con- 
dition when the stresses cease to act. It must not be 
confused with such properties as extensibility or flexibility. 
A glass fibre is much more flexible than a rod of the same 
material ; but their elasticity is the same. 

So long as the stresses and accompanying strains are not 
too large, solid substances behave with fairly perfect elas- 
ticity ; but beyond certain limits, which experience alone 
can determine in any particular case, there is nothing like 
complete recovery when the stresses are removed. Under 



I INTRODUCTION 9 

these conditions we may speak of the substance as being 
quasi-elastic. A simple but instructive illustration of the 
distinction between perfect elasticity and quasi-elasticity is 
afforded by the behaviour of india-rubber under tension. 
This substance, known as elastic in some of its forms, is not 
really more elastic, and, indeed, is in a certain sense less 
elastic, than steel. When the load is gradually increased 
the stretched rubber does not immediately attain its greatest 
extension under a given value of load. When left for some 
minutes it gradually grows in length ; and, similarly, when 
the load is removed, after it has acted for some time, the 
rubber does not immediately recover its original unstretched 
length. Gradually, however, it will creep back towards this 
original length, reaching it after a prolonged interval of time. 
Similar effects are produced when rocks are subjected to 
stresses of various kinds. 

It is clear, then, that seismological phenomena, dealing 
as they do with changes of form of rocks under great 
stresses, demand for their elucidation some acquaintance 
with the facts and theories of elasticity. The more logical 
course would be to enter upon a preliminary discussion of 
these facts and theories. Since, however, the more impor- 
tant applications of the theory of elasticity are required 
only when the modes of transmission of earthquake tremors 
come to be considered, we shall find it more convenient 
to defer discussion of this theory until after the more out- 
standing phenomena of earthquakes have been described. 
To the description of these phenomena we now proceed. 



CHAPTER II 

EARTHQUAKE PHENOMENA 

Immediate and Transient Effects of an Earthquake. Earthquake Sounds. 
Stifling Effect of Viscosity. Destructive Effects. Undulations. Pro* 
jection of Stones. Buildings, Tombstones, Monuments. Vorticity 
of Ground. Horizontal and Vertical Displacements. Contraction 
and Expansion of Areas. Cadastral Surveys. 

IN this chapter we shall first consider the immediate and 
usually transient effects of earthquakes as they appeal to 
the senses of the inhabitants of the districts visited ; and 
then the conclusions which may be derived from a study 
of the permanent effects as illustrated chiefly by damage to 
works of human construction, and by changes of configura- 
tion on land and water. 

It will serve no scientific purpose to describe in rhetorical 
language the earthquake in all its horrors. Words can give 
no adequate idea of the sensations experienced and emotions 
evoked by a quake, even when it is slight and unaccompanied 
by death and destruction. When the shock is severe, causing 
havoc and dismay, the experiences of the unfortunate victims 
beggar all description. 

Probably the most evil feature of the earthquake is its 
suddenness. It is true that in the vast majority of cases 
a severe shock is heralded by a series of preliminary shocks 
of slight intensity. These might be taken as fore warnings, 
if it were not that they occur as a rule in seismically sensitive 
districts where slight shocks frequently happen without 
leading up to a large earthquake. It can hardly be said 
that familiarity breeds contempt ; yet the very frequency 
of these light shocks in countries like Italy and Japan 
disarms the inhabitants of any immediate apprehension of 
a seismic catastrophe. Only after the havoc has been 
wrought does the memory recall the sinister warnings of 
hypogene action. 

A destructive earthquake is always accompanied by sounds. 



II EARTHQUAKE PHENOMENA 1 1 

Sounds are also frequently, though not always, heard with 
moderate shocks which last a few seconds and do little or 
no damage. The great majority of weak shocks, and even 
many fairly strong ones, are unaccompanied by any (audible) 
sound ; on the other hand, earthquake sounds may be heard 
yet no shock be felt. Sometimes the sound precedes, some- 
times succeeds, the shock proper ; at other times shock and 
sound are practically simultaneous. The audibility of the 
earthquake sound will depend no doubt upon the powers of 
audition of the residents in the district visited, but will also 
be conditioned by other factors of a more or less accidental 
nature. Of these we may mention the quiet or bustle of 
the neighbourhood, the hour of night or day, the character 
of the soil or rock in the immediate vicinity. The sensation 
of sound is produced by any sufficiently rapid and sufficiently 
large variation of pressure in the air; and if the sound is 
fairly continuous with an approach to definiteness in pitch, 
the variations of pressure must be approximately periodic 
with a frequency exceeding thirty or forty vibrations per 
second. The disturbance in the air need not be great 
provided its periodicity is sufficiently pronounced. 

The sounds heard during an earthquake have been 
variously described the commonest description being, what 
I have myself experienced, that they are like the rumbling 
of a vehicle. When feeble, they have more of a booming 
character, and when very strong they suggest thunder or 
the rattle of musketry. 

Whatever be the original character of the disturbance in 
the earth, it must first pass into the air as a compression,-! 1 
dilatational disturbance capable of affecting our ears. In 
chapter x, below, it is shown that a very small, perhaps 
not a thousandth part of the energy of wave motion in th< 
rock can pass by refraction into the air. Also since the 
speed of propagation of the compressional wave in air is 
much smaller than the speeds of propagation of elastic wav- 
in rock, the direction of propagation of the wave in air mu-t 
be nearly vertical, however oblique to the surface the elastic 
wave in the rock may come. This at once explains why tin' 
sounds always seem to come from the ground. 



12 EARTHQUAKE PHENOMENA II 

If we exclude for the moment the case of severe earth- 
quakes which produce fissures and cracks in the ground, it is 
evident that the horizontal motion of the ground (except 
in so far as it sets vertical walls into harmonic oscillations) 
can have little if any effect in sound production. The com- 
pressional wave in air must be almost entirely due to the 
vertical motion of the ground. In cases in which sound is 
heard before the shock is felt, the origin of the shock is 
probably at some distance from the locality, so that time 
may be given for the comparatively small rapid elastic 
vibrations to run ahead of the larger quasi-elastic vibrations 
which constitute the sensible shock. There is no doubt 
that such rapid vibrations do run ahead of the larger 
disturbances ; and the reason why audible sound does not 
always precede the shock proper is simply because the 
viscosity of the material stifles the vibrations of short 
periodicity. The nature of the soil and underlying rock 
at a given locality have, indeed, a distinct influence on the 
sound phenomena. Hard rocky soil is favourable to the 
production of sound ; while soft alluvial soil is comparatively 
unfavourable. 

The main factor in the production of earthquake sounds 
must be the intensity of the shock itself. The greater the 
intensity the greater the chance of sounds being heard. 
Dr. Charles Davison 1 has given an admirable account of 
many of the sound phenomena accompanying earthquakes. 
In particular he discusses the data provided in Milne's great 
catalogue of 8,255 Japanese earthquakes, and finds (as was 
of course to be expected) that the percentage number of 
earthquakes accompanied by sounds increases with the 
disturbed area, that is, with the intensity. As the disturbed 
area increased from 100 square miles to 10,000 square miles 
the proportion of shocks accompanied by sounds increased 
from 12 to 70 per cent. It is obvious that, other things being 
equal, the more widely distributed the earthquake the more 
chance there will be of sounds being heard, not only because 
of the greater number of people subjected to its influence, 
but also because it is itself a more powerful shock. Davison 
1 Philosophical Magazine for January, 1900. 



II EARTHQUAKE PHENOMENA 13 

is indeed of opinion that 70 per cent, is a low percentage for 
quakes disturbing 10,000 square miles of surface. This low 
percentage he regards as evidence that the Japanese as a 
people are defective in the power of hearing low sounds. 

In the same paper Davison points out that the compara- 
tively weak shocks which visit Great Britain are almost 
always heard as well at felt indeed sometimes heard only ; 
whereas in Italy there is not the same high percentage of 
audibility even with much stronger shocks. It is interesting 
also to note that the Charleston earthquake of 1886 was felt 
by many who heard no sound ; and this comparative freedom 
from sound was not confined to places remote from the 
epicentre. 

The whole evidence indicates that several factors enter 
into the question. One of these no doubt is the personal 
equation of the observer and recorder. But the italicized 
statement a few sentences back, namely, other things being 
equal, is a necessary qualification in all cases of comparison. 
An earthquake, deep-seated in its origin, may be felt over 
a much larger region of the earth's surface than one origin- 
ating at a much less depth. But it is highly probable that 
the rapid vibrations which are essential for the production 
of sound may be more completely stifled by the viscosity 
of the material as they pass through a greater thickness of 
the earth's crust. Hence a wide-spread earthquake, coming 
from a deep-seated source, may produce no sound pheno- 
mena in places where it is generally felt, whereas a compara- 
tively feeble shock of limited extent and shallow focus may 
be heard even where it is not felt. 

During my eight years' residence in Tokyo, Japan, I felt 
many earthquakes of the moderate intensity which just 
stopped short of doing damage ; but those which were 
accompanied by a rumbling sound distinct from creaking 
of walls and rattling of ornaments were comparatively few. 
Other Europeans resident in Tokyo and Yokohama had the 
same experience. Now, in any general catalogue of Japanese 
earthquakes, those which are felt in the Tokyo- Yokohama 
region constitute a large percentage and cannot fail to 
impart to the whole any marked characteristic peculiar to 



14 EARTHQUAKE PHENOMENA II 

them only. The plain of Musashi is a great stretch of 
alluvial soil, just the kind of material fitted to kill out rapid 
vibratory motion. This consideration seems to be a suffi- 
cient explanation of the comparative scarcity of Sound 
phenomena in Japan, without the assumption of any general 
acoustic deficiency among the Japanese, or among European 
residents in Japan. 

In his account of the Assam earthquake of 1897, Oldham 
mentions that the earthquake was heard, not felt, in the 
mines of the Raniganj coal-fields, although at the surface 
above the shock was universally felt and caused some 
damage to buildings. This is an interesting illustration of 
the fact that the surface movements due to an earthquake 
are greater than the movements underground. The vibra- 
tions of the walls and bottom of the mines were sufficient to 
produce sound waves in the air columns filling the mines, 
but were not great enough to cause motions perceptible to 
the other senses. 

It is obvious on general grounds that viscosity must tend to 
kill out the rapid vibrations ; and Nagaoka's and Kusakabe's 
experiments (see below, chapter ix) on the lack of perfect 
elasticity displayed by rocks are of importance in this con- 
nexion. It has been long known that, when imperfectly 
elastic materials are strained under stress gradually applied 
and then as gradually removed, the measured strain corre- 
sponding to any particular value of stress has a different 
value according as this stress is approached from lower or 
higher values. When we subject the material to a cycle of 
stresses between given limits the graphical representation 
showing the relation between strain and stress consists of 
two distinct curves enclosing an area. This area is the 
measure of the energy lost because of the viscosity of 
material. Now Kusakabe has found that this area is 
distinctly greater in some rocks than in others. A few of 
his curves are shown in the figure. Stress is measured 
horizontally and the corresponding strain vertically. The 
greater the area of the loop, the greater the loss of energy 
due to viscosity. The general result indicates that the 
older rocks are less viscous than the more recent. 



II 



EARTHQUAKE PHENOMENA 



15 



It is clear, then, that the elastic character of the rock 
through which earthquake vibrations are being transmitted 



I 



1 



\ 



ll 

ll 

V 

O V, 



1 3 

M 



FIG. 1. 



must affect the nature of the motions felt and the sounds 
heard. Kusakabe 1 has discussed from this point of view 

Frequency of After-Shocks and Space-Distribution of Seismic Waves 
By S. Kusakabe. Journal of the College of Science, Imperial I 
Tokyo (vol. xxi, 1906). 



16 EARTHQUAKE PHENOMENA II 

the relative frequencies of earthquakes in the centre of 
Japan, and has found evidence of a direct relation between 
the frequencies in contiguous districts and the geological 
nature of the rocks in these districts. 

I propose now to pass in rapid review some of the more 
striking phenomena which characterize destructive earth- 
quakes within the region known as the epicentral tract. 
Here buildings and monuments are overthrown and damaged, 
pillars are rotated, the soil is cracked and fissured, rivers 
are dammed up and lakes are drained, fields are so altered 
as to necessitate re-surveying ; in short, every possible 
change of configuration of the surface of the land may 
occur as an accompaniment of an earthquake. 

Since Mallet made his classical Reports (1850-61) on the 
Great Neapolitan Earthquake, the varied permanent after- 
effects of every large earthquake have been carefully 
examined and recorded by competent observers. From 
these Reports much scientific knowledge has been gained, 
although not perhaps of the kind most desired. At first 
statement of the problem it might seem to be a simple 
enough matter to gather, from the nature of the damage 
done, some fairly definite idea of the direction and strength 
of the shock. But the universal experience is quite other- 
wise. The reasons for this will be apparent as we proceed. 

The wave-like motion of the ground during an earthquake 
has been often described by observers. Take for example 
the following accounts by Dr. Parker and Mr. Blackman 
as given by Major Dutton in his report l of the Charleston 
shock of 1886. Dr. Parker says, ' The vibrations increased 
rapidly and the ground began to undulate like a sea. The 
street was well lighted, . . . and I could see the earth-waves 
as they passed as distinctly as I have a thousand times seen 
the waves roll along Sullivan's Island beach. ... I could 
see perfectly and made careful observations, and I estimate 
that the waves were at least two feet in height .... I saw 
a brick wall . . . reeling from west to east, and am sure 
that it leaned over at times as much as forty to forty-five 
degrees from the perpendicular.' Mr. Blackman set himself 
1 United States Geological Survey, Ninth Annual Report, 1887-8. 



II EARTHQUAKE PHENOMENA 17 

deliberately to study the phenomenon ' at all hazards ', and 
reported as follows : ' After the first vertical tremor had 
passed, and while I was being swayed to and fro by the 
succeeding horizontal movement, I distinctly saw four or 
five separate waves pass across Tradd Street from the north- 
east to the south-west. As nearly as I can estimate the 
width of the several waves, they were about as wide as the 
roadway between the sidewalks ; as to their height, I would 
not like to venture an estimate, but each seemed to be at 
least a foot high.' 

Estimation of wave height in such a case must be extremely 
difficult, for there is no fixed vertical line to serve as standard 
of comparison. The ' two feet in height ' is almost certainly 
overestimated, and probably also the one foot height. But 
even taking the estimates as they are, we see at once that 
the waves must be fairly long and flat, and that it is impos- 
sible for the slope of the ground to attain anything like 
an angle of 45. In forming an estimate of the deviation 
of a wall from the vertical, the observer has the same diffi- 
culty as that already mentioned, the absence of a steady 
vertical line to serve as guide. There is also his own rocking 
motion to be taken into account, as well as the motions of 
surrounding bodies. A particular combination of these 
various rocking motions might quite easily exaggerate the 
apparent motion of a particular wall. There can be little 
doubt, however, that the ground is thrown into distinct 
waves, which may travel partly as gravitational, partly as 
quasi-elastic flexural waves. 

The impulsive motion of the ground is proved by the 
manner in which blocks of stone partially imbedded in the 
soil are loosened and projected several feet from their 
original position. Oldham, in his account of the Indian 
shock of 1897, 1 gives some interesting illustrations of this 
effect. Stones of various sizes were found displaced along 
the level through distances which varied as a rule from 
2 ft. to 4 ft. There were comparatively few cases of smaller 
displacements than the lower limit mentioned, showing that 

1 Memoirs of Geological Survey of India, vol. xxix. 

KNOTT C 



18 EARTHQUAKE PHENOMENA II 

when the impulse was sufficient to loosen the blocks from 
their hold of the ground in which they were half imbedded, 
it was also sufficient to project them through a horizontal 
range of at least 2 ft. A splinter of granite 3 ft. long, which 
had been lying flat on the ground, was projected through 
a horizontal distance of 8*5 ft. ; and an upright monolith 
some 6 ft. high, was shot out of the ground and through the 
air in such a manner as to fall at a distance of 6 ft., a deep 
dent in the ground marking the place where the lower end 
struck. These cases all indicate considerable impulsive 
action of the shock. The smallest velocity of projection 
which will enable a projectile to come to earth at a distance 
of eight feet from the point of projection is 16 ft. per second ; 
and with this combination of initial velocity and range of 
projection the angle of projection would be 45. For small 
speeds of the kind indicated the resistance of the air is 
negligible, so that the projected stone would come down to 
the ground with practically the same velocity as that of 
projection. But the marks made on the ground by the 
falling stone seem to require a higher velocity than 16ft. 
per second. This would imply either a considerably smaller 
or a considerably higher angle of projection. Oldham is of 
opinion that the whole nature of the effect indicates bodily 
displacement of the ground in which the block was partly 
imbedded. Any attempt to explain it in terms of the 
elastic vibrations of the material as the shock impinges 
internally on the surface of the ground leads to values of 
accelerations and elastic displacements which seem to be 
altogether out of the question. The evidence for the 
existence of surface undulations comparable to ocean swells 
has been considered and seems to be incontrovertible. 
The vertical motion of the ground when such waves pass 
along might easily enough be sufficient to project blocks of 
suitable size and mass with velocities exceeding the limits 
given above. It is interesting to note that the blocks which 
were projected were all, within certain assignable limits, of 
a particular average size. When the stone is too small the 
cohesive forces, which depend on the surface of contact 
of the stone and the soil, are proportionately great in 




FIG. 2. INGLIS'S MONUMENT AT CHHATAK. 



II EARTHQUAKE PHENOMENA 19 

comparison with the momentum communicated to the stone 
when the ground has its maximum motion ; for thia momen- 
tum depends on the mass, that is, the bulk of the stone. 
For larger sized stones the cohesive forces, though greater 
absolutely, are less effective in comparison with the mo- 
mentum communicated ; hence a greater chance of these 
becoming loosened and projected through the air. On the 
other hand, when the stone becomes too large, the greater 
mass for the same communicated momentum implies 
a smaller velocity, and projection against the force of gravity 
becomes impossible. 

The effects of earthquake shocks on buildings, tombstones, 
and monuments have naturally attracted a great deal of 
attention on the part of seismologists. It is by careful 
study of these cases of damage or destruction that we gain 
knowledge as to the best methods of construction in earth- 
quake countries. Also from a purely scientific point of 
view we gain information regarding the nature and power 
of the seismic motion itself. With so many typical examples 
in the great earthquakes of Charleston, Japan, and India, 
it is not easy to make a choice. Certain cases described by 
Oldham are, however, particularly instructive. We cannot 
do better than quote his descriptions and reproduce some 
of his diagrams. 

* The most imposing and striking of the numerous instances 
of twisting is that of the monument to George Inglis, erected 
1850, at Chhatak. This conspicuous landmark takes the 
form of an obelisk, and rising from a base 12ft. square, 
must have been over 60 ft. high before the earthquake. . . . 
The topmost 6 ft. 2 in. was broken off and fell to the south, 
while the next 9 ft. was thrown to the east, as shown in 
plan (in Fig. 3). Of the remainder, the top 22ft. has been 
separated at a height of about 23 ft. from the ground, and 
twisted negatively through 30.' 

The general appearance of this obelisk after the earthquake 
is shown in Fig. 2, reproduced from Oldham's photograph. 

In the figure showing the Inglis monument in plan is 
shown also the case of two neighbouring pillars which 
suffered different rotations, the aqueduct pillar being twisted 

C 2 



20 



EARTHQUAKE PHENOMENA 



II 



negatively 5, and the pillar on the wall 4 in the opposite 
direction. 

In Mr. Latouche's Report, which forms Appendix A to 
Oldham's memoir, some remarkable cases of damage to 
tombstones are recorded. One case was that of a small 
marble pedestal supporting a cross. The pedestal was 
twisted round through 26, while the cross fell at the foot. 




FIG. 3. INGLIS'S MONUMENT AT CHHATAK IN ELEVATION AND PLAN, 
AND TWISTED PILLARS AT CHERRAPTJNJI. 

These examples of rotatory effects demonstrate com- 
pletely the great complexity of the movement of the ground. 
Two pillars a few feet apart have been rotated in opposite 
directions and have been displaced in directions almost 
perpendicular to each other. 

This vorticose movement, which at first sight seems to be 



II EARTHQUAKE PHENOMENA 21 

proved by such effects, has not been accepted by some 
authorities. As is well known in dynamics a simple impulse 
or blow acting on a body will cause that body to rotate if 
the impulse does not act through the centre of mass. Hence 
a succession of blows in varying directions may easily cause 
a rotation in a body resting on but not imbedded in the soil. 
But it is difficult to escape from the belief that rotation of 
an object like a pillar or tombstone which is imbedded in 
the soil is an effect shared by the ground itself. Indeed 
how can we have in the ground a succession of blows varying 
rapidly in direction without something of the nature of 
whirling or vorticose motion accompanying it ? 

It is a familiar principle in the motion of a rigid body that 
any displacement can be effected, in an infinite number of 
ways, by means of a translation in a definite direction in 
combination with a rotation about a definite axis. But it 
does not follow that this has happened dynamically. In all 
probability the successive stages through which the highest 
remaining block in Inglis's Memorial passed formed a compli- 
cated sequence of yieldings to successive shocks varying in 
direction and magnitude. 

We may easily imagine a shock of a sudden impulsive 
nature snapping a pillar at some little height and giving it 
a slight tilt on one corner or edge, while at the same time 
the lower part moving with the ground will be both tilted 
and rotated in a manner not generally similar to that in 
which the upper part has been moved. The tilt of the 
upper part is due to the impulsive force acting on it ; but 
the tilt of the lower part is due to its being fixed to the 
ground. We cannot hope to formulate the complex 
dynamics of this problem. A general statement is all we 
can venture on. The rotation and tilting of the support will 
put the two parts out of relation, so that a perfect readjust- 
ment is practically impossible. The chances are that the 
upper part will fall in a direction and with a rotation deter- 
mined by such a complexity of forces as to be practically 
arbitrary. On rare occasions, as in the case of the Inglis's 
Monument, the upper part will remain poised in position, 
but permanently displaced from true adjustment. 



22 



EARTHQUAKE PHENOMENA 



II 



Another illustration from Oldham's Report may be given 
as showing the different directions in which different parts 
may be projected. This is the case of Willan's Memorial at 
Shillong, reproduced in Fig. 4. Mr. Latouche, who reported 
this case and supplied the sketch, was able to identify four 
of the fallen blocks before they had been moved. These 




Frmm. IT ,H 




Plan showing position of 2nd, 3rd, 4th, and 5th blocks from top of obelisk. 
FIG. 4. WILLAN'S MEMORIAL, SHILLONG. 

seem to have been projected one after the other in different 
directions practically without rotation. It is mentioned that 
the blocks left on the top of the portion of the pedestal still 
standing are twisted slightly towards the east. These are 
only a few out of many similar cases which have been 
described by geologists and seismologists. 

To sum up. There can be little doubt that the earthquake 



II EARTHQUAKE PHENOMENA 23 

consists at any one place of different trains of waves passing 
in various directions, the result of internal reflexions and 
refractions of the original complex disturbance. 1 These 
trains of waves will interfere somewhat like trains of ripples 
on a lake, but in a vastly more complicated fashion. The 
resultant effect will in many cases change fundamentally in 
a stretch of a few yards. Here the impulses and accompany- 
ing ground movements will give all the characteristics of 
a whirl or vortex : there they will produce practically pure 
translational effects unaccompanied by any marked rota- 
tional phenomena. The necessary complexity of the motion 
seems to be sufficient to explain all the observed phenomena. 
The final effect upon a pillar or wall or house must depend 

(1) upon the space and time averages of the acting impulses, 

(2) upon the way in which these vary and especially upon 
the accelerations. 

In the Assam quake of 1897, and in the Japanese disaster 
of 1891, striking examples were given of the permanent 
change of areas. The rails of railway tracks, originally 
straight, were distorted into great serpentine folds, demon- 
strating that the soil had contracted. Opposing piers of 
bridges were brought closer at the base while the upper 
portions were kept apart by the resistance to buckling 
presented by the bridge. The same contraction was indicated 
by the buckling of wooden bridges crossing streams or 
swamps. In other cases the piers were drawn apart and 
the bridge collapsed. 

The displacement of neighbouring plots of ground is 
beautifully illustrated by a case described by Koto in his 
memoir on the geological phenomena of the Mino-Owari 
earthquake. 2 Two trees in a garden originally facing each 
other in an east-west line were shifted so as to lie in a north- 
south line. The portions of ground on which the trees 
stood had been shifted relatively north-west and south-east ; 
and yet in this particular place Koto was unable to see any 
line of fault. The neighbouring portions of ground had 

1 See below, chapters ix and x. 

2 Journal of the College of Science, Imperial University of Japan, vol. v, 

1893. 



24 



EARTHQUAKE PHENOMENA 



II 



been simply sheared past one another without the permanent 
production of any recognizable fissure or difference of level. 

Along the surface lines of fault in the two earthquakes 
named above there were found many illustrations of change 
of level. One of the most perfect of these is the Midor Valley 
in Japan, where a 20ft. downthrow occurred right across 
a tea plantation which filled up the broad base of the valley. 

In general, a contraction of area in one district means an 
expansion in a neighbouring locality ; and in the great 
Assam quake of 1897 evidence of wider changes was obtained 
in the re-triangulation of the district. In the diagram 
(Fig. 5) a small part of the triangulation is shown connecting 
the stations Laidera, Mautherrichan, Mosinghi, and Mun ; 
and the following tables show the comparison of the lengths 




MU. 



Mo. 



FIG. 5. 



and heights of the stations according to the surveys of 1860 
and 1898. 



Pairs of 
Stations 


Lengths in feet 


Diff. 

+ 3-9 
+ 2-6 
- 0-3 
+ 1-2 

+ 4-4 


1860 


1897 


L -Ma 

L - Mo 
L - MU 
Ma - Mo 
Mo - Mu 


72,373-1 
64,350-8 
63,007-7 
83,931-8 

84,893-2 


72,377-0 
64,353-4 
63,007-4 
83,933-0 

84,897-6 



II 



EARTHQUAKE PHENOMENA 



25 



Stations 


Heights 
1860 


j in feet 
1897 


Diff. 


Shifts 


L 

Ma 
Mo 
Mu 


6180 
6288 
5794 
6212 


6186 
6312 
5798 
6214 


+ 5 

+ 24 
+ 4 
+ 2 


J.t, N. 
1 ft. N., 5 ft. W. 
3 ft. W. 
4 ft. N. 



These numbers are calculated on the assumption that 
a certain assumed base line had not been altered in length, 
and a certain assumed station not altered in elevation. 
These were chosen to the south so as to be as far as possible 
from the epicentral tract. There is, therefore, a certain 
doubt as to the absolute values given. Nevertheless they 
indicate differential movements of the stations too large 
and too irregular to be attributed to errors of observation. 



CHAPTER III 

SEISMIC SURVEYS 

Collection of Reports. Scale of Intensities. Isoseisms. Laibach, Charles- 
ton, Assam. Determination of Epicentre. Coseismal Lines. Button's 
Discussion of Time Observations. Determination of Depth of Focus. 
Dynamical Measure of Intensity. West's Formula. Milne's and 
Omori's Experiments. Holden-Omori Dynamical Scale of Intensity. 
Dutton's Method of determining Depth of Focus. Davison's Isa- 
coustic Lines. Twin Earthquakes. Harboe's Herdlinien. 

THE work of the seismologist begins when the earthquake 
ends. His duty is to make a careful survey of the district 
visited by the shock ; to collect from those who have ex- 
perienced it all kinds of information as to movements, 
sounds, times, durations, and the detailed character of the 
disturbance ; to consider this information as a whole, cor- 
recting exaggerations, filling in blanks, and comparing 
intensities in the various localities from which records have 
come ; to deduce, if possible, the situation and probable 
depth of the earthquake origin ; and finally to draw con- 
clusions as to the nature of the original disturbance. 

When the disturbance originates underneath inhabited 
land, there is generally no difficulty in determining with fair 
accuracy the part of the earth's surface nearest to the origin 
the so-called epicentre, epicentral or epifocal tract. In 
the case of severe quakes the extent of damage to works of 
human construction indicates this region with great pre- 
cision. The method fails more or less when the epicentre 
lies in an uninhabited or desert region, or even in a district 
with a scattered semi-civilized population. The seismologist 
must then make the best he can of purely geological changes 
such as fissures and cracks. 

With moderate earthquakes causing no damage the 
investigator is compelled to deal simply with the reports of 
those who felt the shock, and by careful and judicious 
comparisons endeavour to fix on the region of maximum 
intensity. It might be supposed that time observations 



Ill SEISMIC SURVEYS 27 

would prove of value ; but practically the great majority 
of time observations, which are not instrumental, lack 
definiteness, because of the inaccuracy with which the 
ordinary individual keeps time. 

When the origin of the earthquake is below the bed of 
the ocean, the difficulty of determining its position is greatly 
increased. As a matter of fact the greater number of shocks 
do originate below the sea ; and the data at our disposal 
derived from reports from neighbouring land stations are 
necessarily incomplete and vague. 

Clearly the first desideratum is some method of measuring 
the intensity of a shock. From a strictly dynamical point 
of view the intensity of an earthquake, as experienced at 
any locality, should be determined by the energy of the 
motion of the ground produced there. But how is this 
energy to be estimated ? 

Consider for example the scale of intensities drawn up by 
Rossi and Forel, and known as the Rossi-Forel Scale. Ten 
grades are distinguished. For present purposes they may 
be described briefly as follows : 

THE Rossi-FoREL SCALE OF INTENSITIES. 

I. Microseismic shock ; instrumentally recorded ; perhaps felt by an 

experienced observer. 
II. Extremely feeble : felt by a comparative few at rest. 

III. Very feeble : felt by a considerable number at rest. 

IV. Feeble : felt by persons in motion, but not generally ; disturbance 

of certain objects. 
V. Moderate : felt by every one ; disturbance of furniture, &c., quite 

general. 

VI. Fairly strong shock: sleepers awakened; persons sufficiently 
startled to leave their houses; clocks stopped; oscillation of 
chandeliers. 

VII. Strong : general panic ; overthrow of movable objects. 
VIII. Very strong : fall of chimneys ; cracks in walls. 
IX. Extremely strong : partial or total destruction of buildings. 
X. Disastrous ; fissures in ground ; ruin and disaster. 

The Mercalli Scale is broadly similar and constructed on 
much the same lines. 

It will be seen that Intensities II to V are determined 
almost entirely by the sensations of individuals ; while 



EARTHQUAKE PHENOMENA 



III 



Intensities VII to X are determined by the degree of damage 
done and the amount of destruction wrought. 

Such a scale of intensity cannot of course be regarded as 
giving a scientific estimate of the energy involved in any 
particular case ; but it has the great merit of being essentially 
practical. When the districts experiencing the shock are 
populous the seismologist has no great difficulty collecting 
information sufficient to enable him to map out the district 




FIG. 6. 

by means of ' isoseisms ' or lines of equal seismic intensity. 
Each isoseism passes through localities at which the in- 
tensity was the same, and forms a closed loop within which 
the intensity was hi general higher than that associated with 
the isoseism. 

In the accompanying figures two earthquakes are shown 
treated in this way, namely, the Charleston earthquake of 
1886 (after Button) and the Indian quake of 1897 (after 
Oldham). In the former the isoseisms could be drawn only 



Ill 



SEISMIC SURVEYS 



29 



on the landward side ; but there is no doubt that it forms 
one of the most completely worked out cases of a destructive 
earthquake. Obviously the isoseism of highest intensity 



Hfe 




FIG. 7. 

encloses the smallest area and indicates with fair precision 
the epicentral region. 

In Oldham's chart of the Indian earthquake 



30 



EARTHQUAKE PHENOMENA 



III 



I have added the approximate isoseisms of the earthquake 
of April 4, 1905. These are shown in the N.W. corner, and 
the limits within which this shock was felt are indicated by 
the full line drawn across India and passing near Bombay 
and Calcutta. 

Taking these examples, and also the Laibach earthquake 
of 1885, very completely worked out by F. E. Suess, let us 
consider the relation of the intensity on the Rossi-Forel 
scale to the average distance of the corresponding isoseism 
from the epicentre. The average distances were estimated 
by drawing a succession of radiating lines from the epicentre 
at equal angular intervals, and measuring the distances 
of the isoseismal lines along these. 



Isoseism 
R. F. scale 


Distance in miles from epicentre at 


Laibach 


Charleston 


Assam 


n 


201 


806 


930 


in 




720 




IV 


142 


585 


800 


V 


108 


469 




VI 


75 


373 




VII 


26 


239 




VIII 


13 


136 


240 


IX 


8 


46 




X 




13 


70 



These numbers, especially in the case of the Charleston 
earthquake, indicate a fairly good approximation to a true 
linear relationship between scale intensity and distance from 
epicentre. If we consider the distances between the same 
limiting intensities for the three cases, we get as follows : 



EARTHQUAKE 


] 
II&IX 


DISTANCE BETWEEN ISOSEISMS 


Av. 


IV & IX 


Av. 


IV & VII 


Av. 


Laibach 
Charleston 
Assam 


193 

760 
730 


28 
109 
106 


134 
539 

600 


27 
108 
120 


116 
346 


39 

115 



It is not possible to give a result for the Assam shock 
between the limits IV and VII, since the intermediate 
intensities are not obtainable with sufficient accuracy. Any 



Ill SEISMIC SURVEYS 31 

attempt to do so would depend on simple interpolation, 
which virtually assumes what it is desired to investigate. 

The columns headed Av. give the average distance 
between the successive isoseisms. They are inversely as 
the average intensity gradient between the assigned limits. 

In both the Laibach and Charleston quakes there is 
diminution of intensity gradient between the limiting 
isoseisms IV and VII. The most interesting feature, how- 
ever, is the much more rapid fall off of intensity with increase 
of distance in the case of Laibach than in the other cases. 
Now when a simple disturbance spreads out in all directions 
from a particular source, we should not expect that the 
original intensity of the shock at the source would affect 
the rate of decay from one lower intensity to another. The 
severe earthquake will, of course, be felt farther than the 
moderate shock, because it begins with a higher intensity ; 
but once the intensity at any locality due to the larger 
shock becomes equal to the intensity that would have been 
produced by a nearer but smaller shock, we should expect 
the rate of diminution thereafter to be very similar. And 
probably this would be so were the shocks dynamically 
similar in beginning, continuation, and finish. But such 
similarity between shocks originating in different places can 
hardly be the rule. It is obvious, for example, that the mere 
duration of an earthquake shock, quite apart from the 
energy of motion taken up by the ground during one second, 
must influence the estimate of the intensity. For the longer 
the shock lasts the more likely is it to be felt by every one. 
A prolonged shock, but not very energetic, might be esti- 
mated higher in the scale than one of shorter duration but 
intrinsically more intense. These considerations show how 
very far short of ideal the Rossi-Forel scale of intensity falls. 
There is a lack of scientific precision about it. Attempts 
to obtain a dynamical measure of intensity will be referred 
to later. 

The highest isoseism determines the epicentre ; but the 
exact localization is usually complicated by the fact that 
the shock has radiated from two or more centres or from 
a long drawn out source of disturbance. The highest 



32 EARTHQUAKE PHENOMENA III 

isoseisms are rarely circular, frequently not even approxi- 
mately so. In the case of the Indian, or Kangra earthquake 
of April 4, 1905, the isoseism VIII consists of two detached 
ovals 50 or 60 miles apart, indicating a twin focus. These 
may be seen in the north-west of India (Fig. 7, p. 29) ; also 
below (Fig. 11, p. 45). 

In the case of the many earthquakes which originate under 
the ocean, the epicentre can be only approximately localized. 
The configuration of the isoseisms as drawn on the neigh- 
bouring land may give some indication, but at the best 
a very uncertain one in the great majority of cases. The 
detailed configuration of any isoseismal line depends upon 
distinctly local conditions, such as the character of the soil 
and the geological structure of the crust. Thus in certain 
cases barriers seem to exist which shield particular districts 
from the disturbance, producing, in short, earthquake 
shadows. 

Much more definite information might be gained from 
a knowledge of the times at which the earthquake occurred 
at several widely scattered localities. This method is, 
however, subject also to considerable uncertainty. First, 
there is the necessity for accurate time-keeping at a sufficient 
number of well-distributed localities ; and, secondly, there 
is the difficulty of identifying at the several localities a par- 
ticular phase of the shock. Generally we must be content 
with the timing of the first impulse or of a marked maximum. 
Assuming, however, that an accurate timing of a definite 
phase is possible at several distinct places, let us consider 
how the information may be used to locate the epicentre. 

Let E be the (unknown) epicentre, and P the position on 
the earth's surface at which the shock is felt at time t. If T 
is the unknown time at which the shock occurs at the epi- 
centre, the difference (T-t) may be regarded to a first 
approximation as the interval of time taken by the shock 
to pass from E to P. Then EP/ (T-t) will be the apparent 
speed of transit of the shock. 1 We may suppose this quantity 

1 For the relation between the apparent speed along the surface and 
the real speed of propagation, see chapter x, p. 173, and chapter xii on 
Seismic Radiations. 




Ill SEISMIC SURVEYS 33 

to be expressed in terms of the data for a number of stations, 
and to be the same in all directions. We then get a series 
of equations 

EPt EP r 
- T=t\ = T=t, = 

the number of independent equations being one less than 
the number of stations. But to locate the position of E 
requires two numbers (latitude and longitude, say), which 
with the time T make three unknowns. Hence there must 
be at least four stations, P^P^P^ at which the times 
^2^4 are known in order that the epicentre may be deter- 
mined. 

The assumptions underlying this method are, strictly 
speaking, not warranted ; and the method could be applied 
only to cases in which the distances (EP) are large compared 
to the depth of the focus. For it is from the focus and not 
from the epicentre that the disturbance radiates. The 
method may be made theoretically more plausible if we 
take the focus F instead of the epicentre E. Then to 
determine F we need three numbers (latitude, longitude, 
depth) hence, including T, four in all. In this case we 
must be given five stations at least. 

When the observations are numerous enough, we may form 
a chart of * coseismal ' lines, each of which is defined as a line 
passing through places at which some definite assignable 
phase of the shock was simultaneous. Milne has used the 
method with some success in determining sub-oceanic origins 
by means of the coseismal lines of the sea waves ; but the 
inherent difficulties of getting sufficiently accurate time data 
prevent the method from being a practical one. Attempts 
have also been made to utilize time observations of the 
shock proper, as transmitted through the earth, and of the 
sea wave started in the ocean above the epicentre ; and 
under specially favourable conditions satisfactory results 
have occasionally been obtained. 

There is no reason why, with the installation of suitable 
recording instruments, the determination of coseismal lines 
should not be greatly increased in accuracy ; but even with 



34 



EARTHQUAKE PHENOMENA 



III 



these accurately determined, the localization by their means 
of sub-oceanic origins must at best be approximate, partly 
because of the generally elongated and asymmetrical form 
of the focus itself, and partly because of the different ways 
in which different rocks respond to the disturbance trans- 
mitted through them. 

As an illustration of the uncertainty which attaches to 
time observations we may take Button's account in his 
valuable memoir 1 on the Charleston earthquake. That 
shock was experienced by a widespread community accus- 
tomed to accurate timekeeping ; and yet on careful examina- 
tion of the records we find many discrepancies which pre- 
vent a satisfactory delineation of the coseismal lines. For 
example, there was a marked tendency for observers to 
reckon by five minute intervals. This is clearly brought 
out in the following table abridged from Dutton. 

Number of Reports giving 9 h. 50m. =32 



10 h. 



51 
52 
53 
54 
55 
56 
58 
59 



= 6 
=25 

=28 
= 31 
=86 
=21 
= 5 
= 3 



Om. = 13 
1=2 



Now the shock happened at 9 h. 50 m. 6 s. at Charleston ; 
hence 32 reports give a time distinctly too soon. But note 
that, though 31 gave the time at 54 minutes past 9 and 
21 gave 56 minutes, as many as 68 gave 55 minutes. Simi- 
larly 13 gave 10 o'clock exactly, whereas only 3 gave 
9h. 59m., and 2 gave 10 h. 1m. These returns show 
a strong favouritism for 9 h. 50m., 9 h. 55m., and 10 h., 
the explanation of which is human, not seismic. By taking 
into account what Dutton regards as the really good time 
observations we are able to draw fairly well the coseismal 
of 3 minutes after the occurrence of the shock at Charleston. 
It is found to run close to the isoseism IV. The average 
distance of isoseism IV from Charleston is 585 miles ; and 
1 United States Geological Survey, Ninth Annual Report, 1887-8. 



111 SEISMIC SURVEYS 35 

this divided by 3 minutes, or 180 seconds, gives the transit 
speed 3-25 miles per second. Button, by applying the 
method of least squares to the two groups of Best Observa- 
tions and Good Reports, obtained respectively 3.236 + 0-105 
and 3-226 0-147. This is in itself a result of great value, 
but it helps in no way to find the depth of the earthquake 
focus. 

Let d be the depth of focus and x the distance of a surface 
point P from the epicentre E, as shown in Fig. 9 on page 40. 
Then, assuming the disturbance to be propagated with 
constant speed, v, through the earth's crust, we find that 
it will reach the position x in time, 



' or f - =, 



The graphical representation of this is a hyperbola with 
vertex at the epicentre, from which, when once drawn, we 
may determine both v and d. But unfortunately neither 
this curve nor any modification of it obtained by assuming 
the speed of propagation to vary with the depth is at all 
applicable to practical cases. The depth of focus of any 
earthquake is probably comparatively small, never exceed- 
ing 20 or 30 miles. It is consequently only within a radius 
of 50 miles or so that the hyperbolic character of the time- 
graph could be detected. When d is small compared with x, 
we have, by expansion of the square root in the first form 

of the equation, t = -(l + 3 +etc.V 

When x = 4 d, the second term in the bracket becomes 1/32. 
With d = 25 and x = 100 miles, the ratio x/v will be some- 
where between 30 and 60 seconds. But very few time 
observations are correct to even 5 seconds, that is, to 
T^-th of the higher limit named. Consequently a difference 
of 1 in 32 is far within the errors of observation. 

As a matter of fact the time-graphs of the Charleston 
earthquake of 1886, and of the Assam earthquake of 1897, 
are practically straight lines, giving the approximate value 
of v, but not giving the least suggestion of the value of d. 

D 2 



36 EARTHQUAKE PHENOMENA III 

The time-graph of the Laibach earthquake of 1895, a& 
drawn by F. E. Suess, shows a distinct concavity upwards 
with a point of inflexion at a distance of 250 kilometres. 
If, however, we take into account only those time observa- 
tions which refer to the beginning of the shock, the time- 
graph is practically a straight line from distance 75 kms. to 
distance 350 kms. This is what we should expect for earth- 
quake origins at depths not exceeding 40 or 50 kms. 

In short, the determination of the depths of earthquake 
origins from time observations is at present a hopeless 
endeavour. Only those within the epicentral tract of 
a destructive shock could be of any use ; but for the time 
records to be of any value they must be certain to 5 or 
10 seconds. The average man, untrained in scientific re- 
search, is satisfied if he knows a time to within half a minute. 
Instrumental records alone will give satisfactory returns ; 
but when the shock is severe the chances are that the 
instruments themselves will be wrecked. The evidence of 
stopped clocks has frequently been appealed to ; but the 
careful sifting of this evidence by Button, in the case of 
the Charleston earthquake, did not lead to consistent results. 

Dutton has himself suggested another method of getting 
an estimate of the depth of an earthquake focus. This 
depends on a consideration of the rate at which the intensity 
of the shock falls off as the disturbance spreads out in all 
directions from the focus and makes its effects apparent at 
the surface. The whole value of the method must ulti- 
mately depend upon the certainty with which we can 
ascertain the rate of decay of the intensity as the distance 
from the epicentre increases. 

The arbitrary and essentially unscientific character of the 
determination of intensities in terms of individual sensations 
has already been referred to. It does not seem to be such 
a hopeless task to deduce dynamical conclusions from the 
overthrow and fracture of chimneys, monuments, tombs, 
walls, &c. It is important, then, to consider the dynamical 
conditions which determine these definite destructive effects. 
The problem was discussed by Mallet and his contemporaries ; 
but little real advance was made till Milne began his 



Ill 



SEISMIC SURVEYS 



37 



-experiments in Japan in 1885. In that year he investigated 
the overturning of blocks and columns which were placed on 
a platform capable of being moved to and fro with simple 
harmonic motions of various amplitudes and periods. The 
results of the experiments are given in volume viii of the 
Transactions of the Seismological Society of Japan. In 1893 
a more elaborate series of experiments was carried out by 
Milne, acting in conjunction with Omori ; 1 and the latter 
has continued the investigation, making use of a platform 
which could be oscillated vertically as well as horizontally. 2 
In all these sets of experiments, columns of various 
dimensions and materials were set on the platform, which 
was then set in motion 
through various ranges and 
with various periods. The 
motion of the platform was 
at the same time recorded 
on a strip of paper moving 
steadily at right angles to 

the direction in which the 

platform was oscillating. 
From the sinuous record 
so obtained, the accelera- 
tion at which the overthrow occurred could be readily 
calculated, and used to test the applicability of various 
formulae for the overthrow of columns. The formula 
which stood best the test was the exceedingly simple one 
due to C. D. West, professor of mechanical engineering in 
Japan. Consider a b!6ck to be on the point of turning over 
by rotation round the edge A (Fig. 8). The effective force 
is the inertia of the block in relation to the horizontal 
acceleration of the ground. If a represents this accelera- 
tion the block relatively to the ground is acted on by a force 
Ma through its centre of gravity in the direction opposil 
to that in which the a6celeration of the ground is taking 
place, where M is the mass of the block. Taking x equal 
to the horizontal distance of the centre of gravity f 

1 See Seismological Journal of Japan, vol. i. 

2 See Earthquake Investigation Committee Publications, No. 4, 1, 



FIG. 8. 



38 EARTHQUAKE PHENOMENA III 

edge A and y equal to its height above A, we have, equating 
moments of forces, 

May=Mgx or a=gx/y 

where g is the acceleration due to gravity 

In the latest experiments carried out by Omori, columns 
of iron, brick, and wood were used, their heights varying 
from a little under 1 ft. to fully 3 ft., and their sections 
square or circular, ranging from 4 ins. to 1 ft. in width. 
Some were hollow and some were solid : and of the forty 
columns experimented with, one only, a hollow column of 
wood, 10 ins. square and 20 ins. high, could not be over- 
turned by the power available. The acceleration of motion 
varied from about 3/4ths to 11 times the acceleration due 
to gravity, that is from 24 to 350 ft. per second per second. 

The general result of the experiments was that the ratio 
of the acceleration expressed by West's formula to the 
actual acceleration which overturned the columns varied 
from 1-5 to 0-7. In 29 cases the ratio fell between 0-8 and 
1-2 ; and in 10 cases the ratio fell outside these limits. 

We may therefore conclude that the overturning power 
of an earthquake shock may be approximately determined 
by means of West's formula, which applies to columns quite 
irrespective of their material. 

Milne also initiated important experiments on the fracture 
of columns. The question was discussed by Mallet in his 
classic, The Great Neapolitan Earthquake, vol. i, page 141. 
By a slight modification of his formula we find, for the 
acceleration necessary to produce fracture in a column of 
thickness 26 ins. the expression 

IF 

= g bhW 

where F is the tensile strength in pounds per sq. in., / the 
moment of inertia of the area about the axis of fracture, 
W the weight of the portion broken off, and h the height in 
inches of the centre of gravity of the fractured part above 
the plane of fracture. 

Both Milne's earlier results and Omori's later results dhow 
that the above formula is fairly applicable. Before the 



Ill 



SEISMIC SURVEYS 



expression can be used we must know the tensile strength 
of the material of the column which has been fractured by 
the shock. 

Basing upon these results Omori has, from his observa- 
tions of damage done in the Mino-Owari earthquake of 1891, 
constructed what he calls an absolute scale of intensities 
a dynamical scale of intensities would perhaps be a preferable 
name. The idea is to express in terms of the amount and 
nature of the damage done the average accelerations of the 
earthquake motion. Holden has made a similar comparison, 
expressing the Rossi-Forel scale in terms of accelerations. 
Remembering that the comparisons are admittedly only 
approximate we may combine Holden's and Omori's con- 
clusions in the following rough table : 



I Rossi-Forel Scale 


Ratio of the 
Acceleration to 


Amplitudes in mm. for 
periods of 




that of Gravity 


Isec. 


2 sec. 


I slight 


0-02 


0-5 


2 


II 


0-04 


1-0 


4 


III 


0-06 


1-5 


6 


IV weak 


0-08 


2-0 


8 


V 


0-12 


2-8 


11 


VI strong 


0-15 


3-8 


15 


VII 


0-30 


7-5 


30 


VIII 


1-00 


25 


100 


IX violent 


2 


50 200 


X 


4 100 



If in accordance with results already discussed (p. 30) 
we assume a linear relation between distance from epicentre 
and intensity as estimated on the Rossi-Forel scale, we shall 
find no clear evidence of a zone of comparatively rapid 
decay of intensity, such as is required for the application 
of Button's method. But in this respect each individual 
earthquake must be judged by itself. Thus Mr. Middlemiss, 
in his preliminary report of the Kangra (or Lahore) earth- 
quake of April 4, 1905, finds evidence for a region of rapid 
decay of intensity in the neighbourhood of the isoseisms X 
and IX The absence of isoseisms of higher name thai 
X seems to me to make this determination very doubtful. 
There ought to be a distinct point of inflexion in the curve 



40 



EARTHQUAKE PHENOMENA 



III 



of intensity such as Dutton indicates in his theoretical 
discussion of the method. This we shall now consider. 

Assuming the disturbance to radiate out in straight lines 
from the focus and neglecting meanwhile loss of energy due 
to viscosity and fracturing, we have the energy at any surface 
point distant x from the epicentre given by the formula 

J- -^~ 



where A is a constant depending on the original energy of 
the shock. Measuring distance horizontally and correspond- 
ing energy vertically, we obtain a representative graph 





FIG. 9. 

which begins convex upwards in the epicentral region, but 
after a certain distance becomes concave upwards. This 
curve is steepest at the point which separates the upward 
convexity from the upward concavity, and here accordingly 
the energy is decaying most rapidly per unit of distance 
outward from the epicentre. Button's energy expression 
being assumed, it follows mathematically that the point of 
inflexion which separates the convexity from the concavity 
and determines the position of the steepest energy gradient 
is at a distance x, which is connected with the depth of 
focus d by the formula d = x V 3. 

But we estimate intensity by damage done to chimneys, 



Ill SEISMIC SURVEYS 41 

walls, monuments, &c. damage which depends mainly upon 
the acceleration, or more accurately upon the horizontal 
component of the acceleration. In simple harmonic motion 
the acceleration is proportional to the displacement, while 
the energy is proportional to the square of the displacement. 
Hence it should be more correct or at least as reasonable to 
use, instead of Button's formula, the expression 

A x Ax 

- x 



But further because of viscosity and fracture there must be 
a more rapid fall off of displacement and acceleration than 
is given by this theoretical formula. A better approxima- 
tion to the truth might be given by assuming a higher power 
of the quantity (x 2 +d 2 ). Let us put 

Ax 

= (x*+d 2 ) 

where n is any number, and find the relation between x and 
d which corresponds to the point of steepest gradient. This 
is found mathematically by equating to zero the second 
differential coefficient of the expression with regard to the 
variable x. This gives 



When n = 1 we have the simplest case in which all loss due 
to viscosity and fracturing is neglected, and we obtain 
dV3 =x, instead of Button's value, d = xV%. For higher 
values of n the ratio of d to x increases. The only result we 
can gain from this argument seems to be that the depth of 
the focus would be about equal to the average radius of the 
ring-shaped zone across which the intensity decays most 
quickly, provided no marked loss of energy occurred. But 
any probable assumption as to loss of energy due to viscosity 
a,nd fracture will increase the ratio of d to x. Hence we 
obtain simply a limiting value for the smallest possible 
depth of the focus. Applying Button's formula to the case 
of the Kangra earthquake, Mr. Middlemiss concludes that 
the long 50 mile focus lay at an average depth of from 
18 to 30 miles, with a dip of 13 or 14 to the horizontal. 



42 EARTHQUAKE PHENOMENA III 

Quite apart from the numerical details which cannot but 
be vague and uncertain, the general principles underlying 
Button's discussion are of interest and importance. The 
deeper the focus the more extensive will be the epicentral 
tract bounded by the highest isoseism. A very shallow 
focus may produce great damage in a small epicentral area, 
but its intensity will decay rapidly with increasing distance. 
Such destructive but comparatively local earthquakes are 
frequently felt in certain parts of Italy. On the other 
hand, great earthquakes with deep-seated sources are felt 
over a wide expanse of country, and by delicate instruments 
can be traced all over the earth's surface. We shall return 
to this question of world-shaking earthquakes in chapters 
xi and xii. 

In addition to the isoseismal and coseismal lines there 
is a third group devised by Dr. Davison and used by 
him with great ingenuity in interpreting certain phenomena 
of moderate earthquakes namely, the is ACOUSTIC LINES. 
These are determined by the percentage of observers who 
heard as well as felt the shock. Thus the line marked 80 
passes through all points in the vicinity of which 80 per 
cent, of the observers of the shock heard the earthquake 
sound. It is only in districts where there are many towns 
that this method can be utilized ; for with few observers 
in a scattered community percentages are meaningless and 
valueless. 

One of the most interesting earthquakes discussed by 
Davison is the Hereford shock of 1896. This was felt over 
practically the whole of England, the intensity of the shock 
in Hereford being sufficient to damage buildings and bring 
down chimneys. The highest isoseismal was No. VIII on 
the Rossi-Forel scale, and enclosed an oval-shaped area 
of 724 square miles, 40 miles long and 23 miles broad, the 
longer axis lying nearly NW. and SE. The chart con- 
structed by Davison is here reproduced. The full lines are 
the isoseismal, and the dotted the isacoustic lines. 

One well marked feature of the earthquake was the double 
shock, which was experienced in all places except those 
lying on a narrow curved zone passing from Devonshire 



Ill 



SEISMIC SURVEYS 



43 



through Hereford towards the east. Its position is indicated 
by the non-closed dotted line on the chart. The simplest 
explanation is that given by Davison, namely, that there 
were two distinct foci originating disturbances almost, but 
not quite, simultaneously. The narrow zone of single shock 
is the locus of points at which the disturbances from the two 
foci arrived at the same instant. Theoretically, if we consider 
the earth's surface to be plane, this line should be a hyper- 
bola, becoming a straight line only when the two shocks of 
the twin-earthquake (as it is called) are absolutely simul- 




FIG. 10. CHART OF HEREFORD EARTHQUAKE. 

taneous. This, for example, was the case in the Derby 
earthquake of 1903. 

In the case of the Hereford earthquake the disturbance 
from the more northern focus was the stronger ; and all 
the relative magnitudes and durations of the shocks and 
the interval between them, as experienced at different 
places, were well co-ordinated by means of this hypothesis 
of the two independent foci. 

The whole subject of twin-earthquakes is discussed by 



44 EARTHQUAKE PHENOMENA III 

Davison in a paper published in the Quarterly Journal of 
the Geological Society for February, 1905. I quote his 
opening paragraph. 

' The essential characteristic of a twin-earthquake is the 
existence of two maxima of intensity connected by weaker 
tremulous motion or the division of the shock into two 
parts separated by a brief interval of rest and quiet. This 
feature, however, is not entirely peculiar to twin-earth- 
quakes ; for, occasionally, one earthquake is succeeded by 
another so rapidly as to simulate a twin-earthquake in this 
respect. A closer investigation of the phenomenon shows 
. . . that the two parts or maxima of a twin-earthquake 
originate in two detached or practically detached foci ; 
whereas in a double earthquake, the foci are either coincident 
or overlapping. ... In all parts of the disturbed area the 
member of a double earthquake which occurs first is felt 
first. In a twin-earthquake, on the other hand, the second 
impulse may, but does not necessarily occur before the 
vibrations from the first focus have reached the other ; so 
that over most of the disturbed area the vibrations first felt 
are those which come from the nearer focus, whether that 
focus was first in action or not. In a double earthquake 
the second shock is a consequence of the first ; in a twin- 
earthquake each is independent of the other.' 

Some of the arguments advanced by Davison may be 
open to criticism ; but the general discussion of the broad 
features of twin-earthquakes is sound and convincing. The 
presence of the zone of simultaneous shock the synkinetic 
band as he calls it which separates two regions at every 
point of which two shocks were felt, is a feature of remark- 
able interest, inexplicable except on the assumption of two 
foci originating disturbances practically simultaneously. 
This synkinetic band will be convex towards the direction 
of the focus first in action. In virtue of the overlapping of 
the isoseisms due to the foci individually, the resultant iso- 
seismal lines, as deduced from observation, present certain 
characteristics, the most noteworthy of which is the way 
in which the higher isoseisms lie excentrically within the 
lower ones. This feature is beautifully illustrated by 
Middlemiss's delineation of the Kangra earthquake already 



Ill 



SEISMIC SURVEYS 



45 



referred to. A small portion of this is reproduced, showing 
apparently a double system of twin-earthquakes. 




FIG. 11. 



The isoseism VIII consists of two oval-shaped lines 20 to 
50 miles' apart ; and within the larger of these the higher 
isoseisms IX and X are situated excentricallv. 



46 EARTHQUAKE PHENOMENA III 

Davison has suggested a theory of the origin of twin- 
earthquakes, connecting their occurrence with the formation 
of the foldings of the crust, and the average distance apart 
of the two foci with the average distance between successive 
anticlinal and synclinal folds. 

The present chapter would not be complete without some 
reference to E. Harboe's ingenious attempt to bring harmony 
out of the chaos of time records of great earthquakes. 1 For 
this purpose Harboe imagines the existence of what he 
calls ' Herdlinien ' or focal lines. These may be regarded 
as the surface projections of the more or less deep-seated 
lines along which the shocks which constitute a given earth- 
quake have their origin. These lines are to be laid down 
from a careful consideration of the noted registered or 
recorded times at which the earthquake shock was first felt 
at the various localities of the earthquake-visited district, 
special attention being paid to the episeismic tract, where, 
with the greater intensity of shock, the times will no doubt 
be more accurately determined. The trend of the isoseisms, 
when these are delineated with sufficient fullness and 
accuracy, is also to be taken into account. Harboe applies 
his method in particular to the Charleston earthquake, the 
Assam earthquake, the Kumamoto earthquake of 1889 and 
one or two others of smaller intensity. The ideas which are 
at the foundation of the method are unquestionably of great 
value and seismologically sound. Unfortunately the working 
out of any case in detail is hampered by many grave difficul- 
ties. First and foremost, there is the lack of accuracy in time 
measurements, referred to above, especially in connexion with 
the Charleston earthquake itself. As regards the particular 
development of focal lines indicated by Harboe in his dis- 
cussion of this earthquake I am quite unable to understand 
how he obtains the focal lines which run out into the sea. 
But again, even suppose we had absolutely accurate time 
observations of the first noticeable tremor which heralds in 
a shock an ideal which is attainable only with instru- 
mental records how are we to take into account those local 
conditions referred to by Harboe himself. As Kusakabe 

1 See Gerland's Beitrtige zur GeophysiJc, Band V, pp. 206-38 (1903). 



Ill SEISMIC SURVEYS 47 

has pointed out, the differences in elasticity and viscosity 
of contiguous strata in a shaken district will bring in dis- 
crepancies in time measurements and dynamical estimates 
of intensity which may quite mislead when the attempt is 
made to lay down Harboe's ' Herdlinien '. Apart altogether 
from the examples given of his method, Harboe's ideas are. 
however, important as a timely argument against the too 
prevalent conception of an earthquake having a limited 
' centre ' of disturbance. 



CHAPTER IV 

INSTRUMENTAL SEISMOLOGY 

Instrumental Seismology. Development of Seismographs in Japan and 
Italy. Realization of the Steady Point. Stevenson's Aseismic Joint. 
Vertical Pendulum. Forbes's Inverted Pendulum. Ewing's Duplex 
Pendulum. Horizontal Pendulum. Bracket Seismograph. Vertical 
Seismograph. Record of Complete Motion. Milne's Horizontal Pen- 
dulum. Omori's Horizontal Pendulum. Wiechert's Seismographs. 
Tanakadate's Vertical Seismograph. Trustworthiness of Record. 

IN the preceding chapters we have referred to the com- 
plicated motion of the ground shaken by an earthquake. 
This was proved by the different rotations experienced by 
neighbouring pillars, as well as by the difficulty the seis- 
mologist experienced when he tried to co-ordinate all the 
observed changes and effects with a view to determine the 
origin and intensity of the shock. The scientific mind, 
however, is not content with those vague indications, but 
sets itself to invent a means of absolutely measuring the 
motions as they occur during the earthquake. Instru- 
ments intended for this purpose are called Seismometers ; 
and the best seismometers are also seismographs, since they 
give a permanent record of the motion. 

The earliest types of seismometer were hardly worthy of 
the name, being simply seismoscopes, or instruments for 
recording the occurrence of an earthquake. The seismo- 
meter, properly so-called, came into being about thirty 
years ago, being rapidly evolved at the hands of the band 
of enthusiasts whom Europe and America sent to Japan 
in the early days of her awakening. Particularly effective 
in this direction were the labours of Ewing, Gray, and 
Milne, who may be said to have created the seismograph 
as a scientific instrument of research. 

Meanwhile in Italy the same subject was receiving atten- 
tion at the hands of Agamennone, Cancani, Vicentini, and 
Grablowitz. 

The Japanese took up with characteristic energy the work 



IV INSTRUMENTAL SEISMOLOGY 49 

initiated by their early teachers and advisers, established 
a chair of seismology in their university, and encouraged 
in every way the theoretical and practical study of earth- 
quakes. 

It is not my intention to give a detailed account of any 
one of the instruments now in use in seismological observa- 
tories. 1 It will suffice to indicate the fundamental prin- 
ciples of construction and to give a general account of the 
more successful devices for obtaining a continuous record 
of a shock. Historic references will be made only inci- 
dentally. 

The mechanical problem to be solved so as to be able 
to measure the earthquake motion is to find a point which 
shall be motionless during the whole motion of the ground. 
How is this ' steady point ' to be realized ? It is obvious 
that in some way we must make use of the property of 
inertia, in virtue of which a body tends to remain in its 
state of rest. That state of rest ceases to exist as soon 
as the body is acted on by some force ; and since the body 
must have some connexion with the earth it is not possible 
absolutely to fulfil this condition of unchanging rest. It 
is not difficult, however, to arrange a mechanism so that 
a certain point of it will not immediately respond to the 
influence of the movements of the ground with which the 
mechanism is of necessity in contact at some part of it. 
The numerous forms of seismoscopes for indicating the 
occurrence of an earthquake are constructed on this simpler 
principle, and they are historically the forerunners of the 
continuously recording seismograph which gives a record 
indicating to a greater or less extent the whole motion of 
the ground during the passing of the shock. 

A few of the more important methods may be briefly 
described. 

There is, for example, the ball and plane combination, in 
which a plane horizontal surface rests on three spherical 
balls which roll on another plane horizontal surface. When 

1 A very complete account to date of the most important Seismographs 
and Seismometers is given, together with a full bibliography, by Dr. R. 
Ehlert in Gerland's Beitrage zur Geophysik, vol. iii, 1896-8. 

KNOTT E 



50 EARTHQUAKE PHENOMENA IV 

the latter moves with the ground, the inertia of the sup- 
ported body tends to keep it in position, the balls rolling 
on the lower plate in the direction contrary to that in which 
the said plate moves. Verbeck, in Japan, adopted this 
method ; and D. and T. Stevenson, the well-known light- 
house engineers, made the method the foundation principle 
of their '. aseismic joint'. When in 1868 this firm was 
invited by the Japanese to put up lighthouse towers round 
the Japanese coast, they were at the same time asked to 
guard against the effects of the numerous earthquakes 
which occurred in that country. To this end they proposed 
to support a conical tower sixty feet high and forty feet 
in diameter at the base upon six steel spheres 4-5 inches 
in diameter. Each sphere rested in a shallow concavity, 
and a similar concavity on the lower surface of the base 
of the tower rested on the sphere. The lighting apparatus 
was independently supported on similar balls. The system 
proved serviceable in places particularly subject to earth- 
quakes ; but at most lighthouses the shocks were found 
not to be so frequent or so serious as to require the use 
of the aseismic joint. 

The same principle was utilized by Gray in his rolling 
sphere seismograph. The base was part of a spherical 
surface, and near the centre of the sphere of which the 
surface was a part a heavy weight was pivoted in such 
a way that the pivot point remained practically steady 
when the earth's surface moved to and fro under the spheri- 
cal base, making it to roll. A lever passed from the pivot 
through a point on a bracket fixed to the earth and then 
downwards till it met a smoked glass surface over which 
it moved, giving a magnified record of the relative motion. 

Another important means of getting a temporarily steady 
point is to use a pendulum with a massive bob. This 
massive bob tends to remain steady when the ground is in 
motion. To get satisfactory results from the pendulum 
seismograph it is necessary to use a long pendulum, and 
the longer the better. The Italian seismologists have made 
the pendulum the basis of their elaborate instruments. 
A heavy mass, weighing it may be 200 pounds or more, is 



IV INSTRUMENTAL SEISMOLOGY 51 

suspended by three metallic suspension rods, which in 
certain cases are about 50 feet long. These rods are united 
above to a brass cap which hangs by a steel wire. Such 
a pendulum will have a to-and-fro oscillation of about 
eight seconds period. The point from which the pendulum 
hangs is of course a part of the earth and will partake of 
the motion of the ground. Under certain conditions, 
frequently realized, this motion begins to set up a proper 
motion in the pendulum bob, which can then be no longer 
regarded as a steady point. There may be a marked 
resonance effect (see below, pp. 72, 73). The quick vibra- 
tory motions which characterize many earthquakes will 
produce very little resonance, and for these the pendulum 
may be regarded as a fair approximation to a steady point. 

The relative motion of the ground and the pendulum 
bob is recorded by means of a light lever set vertically 
immediately below the bob. The upper end of this lever 
is fixed to the bob and is the fulcrum. A point a little 
below is in connexion with a support which is fixed to the 
wall of the observatory, and this point accordingly moves 
with the earth. The lower end of the lever is prolonged 
so as to multiply the relative motion about five times. 
This motion, which experience shows to be very complex, 
takes place in all azimuths ; but by an ingenious device 
it is decomposed into two rectangular components by 
means of two other levers which are influenced by the first. 
The further ends of these two levers trace out their move- 
ments on steadily moving strips of blackened paper ; and 
in this way a record of the relative horizontal motion of 
pendulum bob and ground is obtained magnified about 
fifty-fold. 

To get the vertical motion Vicentini adopts a method 
which will be described later when we come to discuss 
the instruments invented by the British investigators in 
Japan. 

Agamennone's vertical pendulum seismograph is identical 
in principle with Vicentini's but differs greatly in detail. 
The recording levers are set above the heavy cylindrical 
bob, and are arranged to make two sets of records, one on 

E 2 



52 EARTHQUAKE PHENOMENA IV 

slowly moving paper and another on rapidly moving paper. 
For the sake of economy the rapidly moving paper is 
started automatically by the earthquake vibrations, which 
through their influence on a delicate seismoscope makes an 
electric connexion and starts the driving clockwork. 

As already stated, the problem is to get a steady point. 
Avith respect to which the relative motion of the ground 
may be recorded and measured. As a practical piece of 
mechanical construction this resolves itself into the problem 
of adjusting a body in a position of equilibrium of small 
stability. The position must be one towards which the 
body after displacement tends to return ; but the restoring 
force must be as small as possible, and the natural period 
of swing as long as possible, consistent with the other con- 
ditions which must be practically realized. For example, 
in the case of the vertical pendulum the stability is dimin- 
ished by making the pendulum very long. But since the 
period varies with the square root of the length of the 
pendulum, it is obvious that there are practical limitations 
to an increase of the period by this means. Thus to get 
a pendulum to make its half swing in ten seconds we should 
have to make the length 100 times the length of the seconds- 
pendulum, that is nearly 4000 inches or 330 feet, a length 
altogether out of the question. This, in fact, is the one 
disadvantage of the vertical pendulum seismograph, that 
we must be content with a stability involving a period 
small enough to be frequently met with in earthquake 
vibrations. 

There are, however, other methods of attaining a long 
swing period, of which the Duplex Pendulum and Hori- 
zontal Pendulum Seismographs are the embodiment. 

In 1841, in a paper communicated to the Royal Society 
of Edinburgh, Professor J. D. Forbes, after commenting on 
the inadequacy of the ordinary pendulum for indicating 
earthquake movements, describes a form of inverted pen- 
dulum seismometer, which is of interest historically as the 
first scientific attempt to get an approximately steady 
point. One of the instruments constructed by him is now in 
the Natural Philosophy Museum of Edinburgh University. 



IV INSTRUMENTAL SEISMOLOGY 53 

It was intended to be used at Comrie in Perthshire for 
registering the first shock of an earthquake. 

His description, slightly paraphrased, is as follows : A 
vertical metal rod, having a ball of lead movable upon it, 
is supported upon a vertical cylindrical steel wire, which is 
capable of being made more or less stiff by pinching it at a 
shorter or greater length by means of a screw. By adjusting 
the stiffness of the wire or the height of the ball we may 
alter to any extent the relation of the forces of elasticity 
and gravity, and consequently render the equilibrium in 
a vertical position stable, neutral, or unstable. The vibra- 
tory motion of the pendulum relatively to the ground is 
registered by a pencil placed in the prolongation of the 
metal rod and adjusted so as to trace the relative motion 
on a spherical dome of copper lined with paper. 

Forbes works out the mathematical theory of the instru- 
ment in considerable detail. Two forms of the instrument 
were constructed, a large and a small, and were set up at 
Comrie ; but apparently no results of value were got from 
them, probably because the Comrie earthquakes were 
neither numerous nor strong enough. Nevertheless Forbes 
clearly recognized the dynamical principle by means of 
which the sensitiveness of the pendulum could be almost 
indefinitely increased. 

For further development along these lines we must go 
to Tokyo in the early eighties. Various suggestions were 
made by Gray and Ewing ; but the most successful method 
for reducing the stability of a short pendulum was that 
devised by Ewing and known as the Duplex Pendulum. 

' It consists of a combination of a common with an inverted 
pendulum. The common pendulum is stable : the in- 
verted, with a rigid pivoted supporting rod, is unstable : 
by placing an inverted pendulum below a common pen- 
dulum and connecting the bobs so that any horizontal 
displacement must be common to both, we may make the 
equilibrium of the jointed system neutral or as feebly stable 
as may be desired. 5 Several forms of this instrument were 
devised by Ewing, and other modifications and improvements 
were effected by Milne. The aim of these modifications 



54 



EARTHQUAKE PHENOMENA 



IV 



was to make the instrument more compact, simplify the 
method of recording the movement, and diminish as far as 
possible the friction at the points and surfaces. 

A diagram of Milne's latest form is reproduced from his 
original description in the Transactions of the Seismological 
Society of Japan (vol. xii, 1887). 

The vertical pendulum consists of a heavy ring W sus- 




FIG. 12 

pended by three threads. The inverted pendulum is 
pivoted at a little below W and passes through a cross 
bar in it, being kinematically connected with the ring by 
means of a ball and socket joint. It is continued above 
and is adjusted by means of a small brass weight which 
can be screwed to the rod in any position. By a suitable 
arrangement the rod of the inverted pendulum is con- 
tinued downwards past the pivot and forms a multiplying 



IV INSTRUMENTAL SEISMOLOGY 65 

lever the lower end of which rests lightly on a surface of 
smoked glass t. When the tripod stand is shaken the 
pivot moves relatively to the bob W , and this motion is 
magnified in the tracing produced on the smoked glass. 

By setting a duplex pendulum on a rocking table, the 
motion of which was registered relatively to the ground at 
the same time by a lever constructed on the same principle 
as the prolongation downwards of the inverted pendulum 
just described, Milne made a series of interesting experi- 
ments which tested the accuracy of the record given by 
the duplex pendulum. The comparison was very satis- 
factory, showing that the duplex pendulum record repro- 
duces with fair accuracy any to-and-fro horizontal motion 
of the ground. When we come to discuss Galitzin's more 
recent experiments of the same nature, we shall find that 
the reason for this fairly faithful reproduction of the 
motion of the ground is due to the relatively high -amount 
of friction involved in the writing of the record. 

The records of the duplex pendulum are very confused, 
and little can be made of them except the direction or 
directions of greatest movement and the amount of the 
movement. It is not possible to determine the periods 
involved. The instrument has more the character of a 
scientific toy than of a really efficient seismometer. 

As a means for obtaining a complete record of the whole 
horizontal movement the duplex pendulum is far inferior 
to the bracket seismograph or horizontal pendulum, the 
successful application of which to earthquake measurement 
was first accomplished in Japan by Ewing. 

The principle of the horizontal pendulum when the move- 
ments are horizontal is a simple piece of dynamics. Imagine 
an impulse / to act on a mass m at a distance x from the 
centre of mass. Its effect is to start the centre of mass G 
with a velocity I /m in the direction of the impulse, and to 
set up an angular velocity equal to Ix/(mk 2 ) in the plane 
containing the centre of mass and the impulse. Here k is 
the radius of gyration and mk 2 the moment of inertia with 
reference to the axis through G perpendicular to the plane 
just referred to. 



56 EARTHQUAKE PHENOMENA IV 

Now this combination of motions of a rigid body can be 
represented by a rotation about a definite axis known as 
the instantaneous axis of rotation. It will pass through 
a certain point C, such that the distance CG multiplied by 
the angular speed will be equal to the linear speed of G. Hence 
linear speed / Ix k 2 

G Or = , = : , o = * 

angular speed m mlr x 

This point or line C is therefore for the moment at rest, 
and if we connect it in some manner with the ground we 
shall be able to observe and record the relative motion of 
the two, which at the start is the real motion of the ground. 
The principle was practically realized by pivoting a heavy 
body so as to be capable of motion 
about a nearly vertical axis. The ends 
^^ ... of this axis were pivoted to supports 
^ * in connexion with the ground ; and 
from the heavy body a light lever was 
carried so as to give a magnified record 
of the relative motion of the body and 
the earth. It was necessary to place 
the axis a little off the vertical, lean- 
ing in fact somewhat towards the 
heavy body, so as to give to the heavy 
body and recording lever some amount 

of stability. Otherwise it would have been impossible for 
the horizontal pendulum to retain a definite azimuth. Un- 
fortunately, as we shall see below, the existence of a certain 
degree of stability brings in the phenomenon of dynamical 
resonance. 

One instrument of this kind is sensitive to motion per- 
pendicular to the line joining the axis of suspension and the 
steady point. To obtain a complete measurement of the 
horizontal motion of the earth we must have two such 
instruments set in perpendicular directions. The horizontal 
pendulum which points north or south will show the east- 
west movement, and the one pointing east or west will 
show the north-south movement. 

In Ewing's form of instruments the ends of the recording 
levers trace out concentric circles on a revolving glass plate 



IV INSTRUMENTAL SEISMOLOGY 57 

kept in motion for a particular period of time by means of 
clockwork. The first tremors of an earthquake acting on 
a delicate seismoscope complete an electric circuit, which 
releases the glass plate and allows the clockwork to drive 
it for four or five minutes. The pointers, resting lightly on 
the smoked surface, trace out a sinuous line oscillating about 
the continuous circle which would have been traced had no 
earthquake been in action. The one inconvenience of this 
form of recorder is that with a quake lasting a longer time 
than the period of revolution of the glass plate the tracing 
by any one pointer will begin to over-write itself, and 
there may be some difficulty in disentangling the separate 
parts of the mingled record. It was with such an instru- 
ment, however, that the first satisfactory records of earth- 
quake motion were obtained. 

With two horizontal pendulums or bracket seismographs 
recording simultaneously on the revolving plate, the com- 
ponents of the horizontal motion only were recorded. It 
was essential to record also the vertical motion. This 
proved a more difficult problem than the recording of the 
horizontal movement. Indications of vertical motion were 
first obtained by the use of vertical springs variously loaded ; 
but such spring-suspended loads once started were set 
oscillating up and down with their own periods of oscil- 
lation, and were thus useless for giving any real continuous 
record of an earthquake motion. Suppose, for example, that 
the load hangs at the end of a vertical spring. To make 
a load suspended in this way at all efficient as a seismoscope 
it is necessary to increase its period of vertical oscillations 
to the utmost. But the period of a heavy load at the end 
of a vertical spiral spring depends, inter alia, upon the 
amount by which the spring is extended by the load. To 
get a slow period we must use a very long spring, so that 
the amount of extension is large. Clearly this method is 
practically incapable of useful development. 

We owe to Thomas Gray 1 an ingenious modification of 
the spring suspension by which the problem of getting 
a steady point for vertical motions was solved. Instead 
1 Transactions of the Seismological Society of Japan, vol. iii, 1881. 



58 EARTHQUAKE PHENOMENA IV 

of hanging the heavy body to the end of the spring, Gray 
used the spring to keep in a horizontal position a weighted 
rod with one end pivoted to a vertical support. Let O 
(Fig. 14) be the pivot, A the point of fixture of the spring, 
and G the centre of gravity of the weighted rod. For any 
small motion about the horizontal position it is easy to 
see that the moment of the weight about remains prac- 
tically constant, but that the moment of the force of the 
spring diminishes or increases, because of the change of 
length, according as the motion is up or down. It is there- 
fore not possible to get a sufficiently small stability by this 
means. By suitably fixing to the rod a trough containing 
liquid, the to-and-fro motion of which altered the distribu- 
tion of weight, Gray was able to get as small a stability as 
was required. A consideration of the fundamental principle 
involved in this arrangement led Ewing a few months later 
to a simpler solution of the same problem. What was 
wanted was to arrange matters so that the upward elastic 
pull of the spring and the downward pull of gravity should 
have equal moments about the pivot for all small motions 
in the neighbourhood of the horizontal position of the rod. 
It is curious to note, as an example of the circuitous path 
by which the human mind frequently attains its object, 
that Ewing's solution of the problem would have come at 
once if it had not been for the apparent simplicity of attach- 
ing the spring to a point in the line joining the pivot and 
the centre of gravity. In short, the less simple arrange- 
ment, in which 0, A, and G are not in the same line, proved 
the simpler in the end for the purpose aimed at. 

The principle may be demonstrated in the following 
simple manner. Let OA G represent the rod and weight 
with centre of gravity at G, pivot at ; and let the spiral 
spring be attached at A, which does not lie in the line OG. 
Then it is clear that an upward motion into the position 
A'OG' indicated by the dotted lines will, while shortening 
the spring, increase the leverage about 0. In like manner 
for a downward motion the lengthening spring will act 
about with a smaller leverage. By a proper adjustment 
the changing value of the force of the spring due to change 



IV 



INSTRUMENTAL SEISMOLOGY 



59 



of length will be accompanied by a change of distance from 
the pivot, so that for small displacements the moment of the 
elastic pull will be as constant as the moment of the weight. 
With the invention of the vertical motion seismometer 
it was possible now to obtain a complete record of an earth- 
quake movement. This was first accomplished by Ewing, 
who arranged two bracket seismographs and the vertical 
motion seismometer to record by means of light levers on 
the same rotating smoked glass plate. Each pointer traced 
out a sinuous record by removing the lampblack from the 
part acted on. The record was then transferred to a sheet 
of sensitive paper by simply laying the glass plate over it 
in daylight, and developing and fixing in the usual way. 



0^ 




-<;' 



FIG. 14. 

One of these complete records is shown in Fig. 15, very 
much reduced in size in the ratio of 4 : 21. 

As already noted, the overlapping of successive parts of 
the record of a prolonged shaking is a disadvantage in the 
original form of revolving glass plate adopted by Ewing. 
In some forms of instruments the record is taken on smoked 
paper wound round a revolving cylinder, to which is given 
a slow translational motion in the direction of its axis. 
Probably the best method is to draw a strip of paper over 
the drum, so that the whole record is obtained in a single 
continuation. Such mechanical methods of taking the 
record introduce of necessity a certain amount of friction ; 
and inventors have as a rule tried to reduce the frictional 
effects to a minimum. 

The ordinary Ewing or Milne-Gray seismographs have 
proved very serviceable in Japan for recording the fre- 



60 



EARTHQUAKE PHENOMENA 



IV 



quently occurring moderate earthquakes ; but it was soon 
found necessary to get still more delicate instruments if 
the smaller motions and pulsations of the ground were to 
be recorded. In the development of these more sensitive 




Diagram of Horizontal and Vertical Motion of the Semi-destructive Earth- 
quake of June 20, 1894 (Tokyo). The wave lines on two inner circles indicate 
the Horizontal, and that on the outermost circle the Vertical Motion, all in 
actual dimensions. The plate revolved once in 118 seconds: the numerals on 
short radial lines mark the successive seconds of time from the beginning. 

FIG. 15. COMPLETE EABTHQUAKE EECOBD (EwiNG INSTRUMENT) 
REDUCED 4:21. 

forms of seismograph the method of support of the hori- 
zontal pendulum has been modified in a way first suggested 
by Gray. Instead of a rigid frame for the support of the 
heavy body, the horizontal pendulum was pivoted at its 
one end and was retained in the horizontal position by 
means of a tie stretching from the neighbourhood of the 



IV INSTRUMENTAL SEISMOLOGY 61 

heavy weight to a point nearly vertically above the pivot. 
The nearer the point of attachment to a truly vertical 
position above the pivot the more delicate and the less 
stable will the horizontal pendulum be, and the better 
fitted for recording small motions. An important form of 
instrument is that devised by Milne and used for recording 
the far travelled tremors of large earthquakes. These will 
be discussed in chapters xi and xii ; but here it is convenient 
to describe the instrument. 

Milne's Horizontal Pendulum consists of a nearly hori- 
zontal boom suitably weighted and pivoted with as little 
friction as possible on its one end. The boom is supported 
by a tie which is fixed to a point nearly but not quite verti- 
cally above the pivot. By means of levelling screws on 
the base plate supporting the upright on which the boom 
pivots, the boom can be accurately directed towards a given 
direction and its small stability can be adjusted to a con- 
venient amount. The weight attached to the compara- 
tively light boom acts as a steady point ; and any horizontal 
motion at right angles to the boom, as well as a tilting 
motion about an axis parallel to the boom, may be recorded 
if there is sufficient magnification of the relative motion of 
the boom and the upright on which it pivots. 

In the Milne form of instrument, the boom is continued 
beyond the tie a considerable distance, and the outer end 
carries a small horizontal disk of blackened mica, which 
has a slit in it cut parallel to the boom. This mica *will 
move relatively to the ground with a motion which is a 
magnification of the relative motion of boom and ground. 
It is arranged to swing over a slit in the lid of a box, this 
slit being at right angles to the slit in the mica. In the box 
a band of bromide paper is driven by clockwork so as to 
be passing continuously under the slit. The light from 
a small benzine lamp is reflected by means of a mirror 
downwards through the two slits and falls on the paper 
as a point of light. When the boom is steady this point 
of light traces what becomes after development a straight 
line on the moving paper. When the boom is in motion 
relatively to the fixed earth the line traced out on the 



EARTHQUAKE PHENOMENA 



IV 



moving paper is of a more or less sinuous character, 
reproducing faithfully the to-and-fro motion of the boom 
relatively to the earth. 

The time record is given by a watch with a long minute 
hand tipped with a piece of blackened mica, which once 
an hour eclipses the light entering the one end of the slit 
on the box. In some forms two slits are made on the mica 
disk, one broad and the other narrow. The fine line gives 



Mirror 




9 Watch 


~S 


Stand 


Boom ^ ? ^ 


T 


^3 



FIG. 16. 

beautiful definition for slow or moderate movements, but 
may fail to produce a photographic impression when the 
motion is rapid. In this case the broader line is necessary. 

The sensitiveness is adjusted until the period of free 
oscillation of the boom is about 15 seconds. 

Some examples of records taken by the Milne Horizontal 
Pendulum are given below in chapters xi and xii. 

The advantages of Milne's form of instrument are its 
comparative cheapness, its simplicity of construction, and 
the ease with which it can be installed and attended to. Its 



IV INSTRUMENTAL SEISMOLOGY i>;j 

sensitiveness is just about sufficient for the purpose aimed 
at, which is to obtain records of motions due to distant 
earthquakes. Its freedom from frictional restraints renders 
it quickly responsive to slight movements of the ground. 

A more substantial form of horizontal pendulum has 
been constructed by Omori ; and as he and his assistants 
have with its aid carried out investigations of the highest 
importance, it is necessary to give a description of its salient 
features. A diagram is shown in Fig. 1 7 one-tenth natural size. 

In designing his instrument Omori aimed at constructing 
a seismometer capable not only of recording ordinary 
earthquakes of the moderate type frequent in Japan, but 
also of registering the smaller and slower movements of 
which the Ewing or Milne-Gray type of seismometer failed 
to give any record. For reasons which need not be 
given here, Omori decided to use the mechanical and not 
the photographic method of taking the record. This is 
effected by means of a light lever designed and constructed 
with great attention to mechanical details. It is pivoted 
about a vertical axis fixed to the ground in the neighbour- 
hood of the heavy weight which forms the steady point of 
the horizontal pendulum. The pendulum itself is suspended 
in the same manner as in Milne's instrument, the mecha- 
nism for adjustment being planned with great care. The 
longer arm of the writing lever is suitably weighted with 
a small mass and presses lightly on the smoked paper 
wound round the revolving drum. The shorter arm of the 
writing lever is in contact with the heavy weight. Any 
relative motion of the horizontal pendulum and the ground 
is increased in the ratio of the arms, namely 1 to 10. A 
diagram of the essential connexion is given below on p. 70, 
where the theory of the instrument is under more particular 
consideration. The instrument is more massive than 
Milne's form, and requires for its support a well-built base- 
ment. The cylinder is run at a fairly high speed, so that 
beautiful open records are obtained. Some examples of 
these are given in Figs. 37 and 38. 

Dr. E. Wiechert of Gottingen, who has in recent years 
given a great deal of attention to the theory and practical 



EARTHQUAKE PHENOMENA 



IV 



details of seismographs of all kinds, has designed several 
new and improved types. In one of these a weight of 
17,000 kilograms is suspended by three fairly thick iron 




FIG. 17. 



rods, the upper ends of which are fixed to an iron frame 
which moves with the earth. The heavy mass which acts 
as the steady point has sufficiently free horizontal move- 
ment because of the elastic yielding of the suspending rods. 



IV INSTRUMENTAL SEISMOLOGY 65 

The relative motion may be magnified several thousand 
times. The greatness of the mass which forms the steady 
point renders the effects of friction at the supports and 
at the mechanical registering apparatus practically in- 
significant. In his memoir on the theory of automatic 
seismographs, published in 1903, 1 Wiechert gives the dynami- 
cal theory of seismographs of all kinds of forms, and his 
instruments are the practical outcome of these important 
studies. Especially noteworthy is his introduction of a con- 
trollable method of ' damping ' the oscillations, the necessity 
for which is discussed in the next chapter. 

In an interesting modification of the vertical motion 
seismograph, due to Tanakadate, two spiral springs are 
used instead of the long vertical helical springs. These 
spiral springs act with opposite moments on the ends of the 
weighted horizontal bar which constitutes the steady point. 
The necessary sensibility is approximately obtained by 
winding up the spiral springs so as to act with the appro- 
priate moments, and is finally adjusted by means of sliding 
pieces on vertical rods attached to the ends of the horizontal 
bar. The effects both of horizontal motion and tilting are 
perfectly eliminated. 

In regard to all forms of seismograph the obvious criti- 
cism is, to what extent are their records a faithful repro- 
duction of the motion of the ground ? As stated above, 
Milne tested the action of the duplex pendulum by placing 
it on a platform which could be made to imitate the to-and- 
fro motion of an earthquake. Others have used the same 
tests ; and in the case of most of the better forms of the 
less delicate seismographs for recording the movements 
accompanying felt earthquakes the seismograph has re- 
sponded with fair accuracy to the motion of the ground. 
Recently Prince Galitzin has made an interesting series of 
tests of the same nature in connexion with his elaborate 
discussion of the dynamical theory of the horizontal pen- 
dulum. His conclusions deserve the fullest consideration. 

1 Abhandlungen der Konigl. Gesellsch. der Wissenschaften zu Gottingen. 



KNOTT 



CHAPTER V 

SEISMOMETRY 

Dynamical Theory of the Horizontal Pendulum. Analysis of Motions. 
Tilting and Horizontal Movement inseparable. Galitzin's Discussion. 
Effect of Frictional Resistances. Omori's writing Lever. Galitzin's 
Experiments. Galitzin's Results. Theory of Forced Vibrations. 
Distinction between Static and Kinetic Sensitiveness. General 
Conclusions. Application to Seismograms. Untrustworthiness of 
Horizontal Pendulum Records. 

THE dynamical theory of the horizontal pendulum is not 
simple, although the main features of its action are readily 
enough understood. Approximate solutions have been 
given by various investigators. We owe the most com- 
plete discussions to Wiechert and to Galitzin, who took up 
the subject almost simultaneously and quite independently 
of each other. Wiechert's memoir has been referred to in the 
last chapter. Galitzin's two memoirs, in addition to general 
discussions having much in common with Wiechert's 
investigation, give in a masterly manner not only the 
dynamical theory of the horizontal pendulum but also 
the experimental test of the theory. The first On Seismo- 
metrical Observations appeared in 1902, and the second 
On the Method of Seismometrical Observations in 1904. 1 

To fix our ideas let us suppose that the horizontal pen- 
dulum is set so as to point north and south, and that the 
line PT from the pivot P to the point T of attachment of 
the tie makes a small angle of inclination i with the vertical . 
If the effective length HP of the horizontal pendulum is 
Z, the period of free oscillation is given by the formula 



p. a, /-i 

Yf 



When the boom HP is slightly displaced it will move to 
and fro in this period. It is clear that the period may be 

1 Comptes Rendus des Seances de la Commission Sismique Permanente 
(Imperial Academy of Sciences, St. Petersburg), vol. i. 



SEISMOMETRY 



67 



greatly lengthened by making i small enough. It is this 
power of adjustment of stability which gives to the hori- 
zontal pendulum its chief merit as a seismometer. I pro- 
pose to call the angle i the stability angle. 

The kinds of movement of the ground to which this 
instrument will obviously respond may be classified thus : 

(1) a rotation about the vertical axis, 

(2) a horizontal movement of the ground in an east and 
west direction, 

(3) a tilting of the ground about a north and south axis. 
Each of these will produce an 

apparent displacement of the 
boom of the horizontal pendulum. 
But if these movements exist, the 
sensitiveness of the instrument 
and therefore the nature of its 
indications will be influenced by 
movement of the ground in a 
north and south direction and by 
a tilting about an east and west 
axis. For example, this tilting 
will alter the angle of inclination 
i and will therefore change the 
stability of the pendulum. 

For a complex movement of 
the ground the behaviour of the 
horizontal pendulum will depend 
more or less on all these parts of the motion which have 
been named, namely, the components of the horizontal 
movements, and the rotations about the three axes, north- 
south, east-west, and vertical. Of these the three move- 
ments tabulated above are of the nature of forced vibrations 
impressed upon the horizontal pendulum. We shall dis- 
tinguish them as the primary disturbances, the other 
movements which influence the behaviour of the horizontal 
pendulum being of a distinctly secondary significance. 

When, as in the case of the bracket pendulums used in 
Japan for recording moderate earthquakes, the inclination 
i is not very small, so that the period is about 3 or 4 seconds, 

F2 




FIG. 18. 



68 EARTHQUAKE PHENOMENA V 

the secondary effects are insignificant. But when the 
sensitiveness of the instrument is increased until the period 
of free oscillation exceeds 12 or 15 seconds, these secondary 
effects cannot be neglected; and when, as in Omori's form 
of horizontal pendulum, the period is as great as one minute, 
the secondary effects due to tilting about the horizontal 
axis at right angles to the boom, or to movements of the 
ground in the direction of the boom, may become very 
significant. 

As regards the primary effects, Galitzin strongly em- 
phasizes the fact that it is impossible to separate the effect 
of the purely horizontal movement from that of the tilting. 
It is not possible, in fact, to draw any sure conclusions as 
to the motion of the ground from the indications of the 
records obtained with the horizontal pendulum as ordinarily 
constructed. If purely horizontal motion or a purely 
tilting movement alone existed some approximate con- 
clusions might be deduced ; but when both exist simul- 
taneously their effects cannot be separated. 

The mathematical proof of this depends on the fact that, 
in the equation of motion of the horizontal pendulum 
pointing north, the term which contains the acceleration 
of the east-west motion also contains a multiple of the 
angular displacement about the north-south axis. If we 
represent the acceleration by the letter a and the angular 
displacement by the angle $, the term is of the form a + gty, 
where g is the acceleration due to gravity. Suppose for 
simplicity that each is of harmonic type and, as is highly 
probable, of different period. Then each will be a forced 
vibration producing on the horizontal pendulum an effect 
which will depend on the value of each period as compared 
with the free vibration period of the pendulum. The 
effects produced on the pendulum by these coexisting 
forced vibrations will therefore not be simply proportional 
to the amplitudes of the corresponding earth movements. 

A point which is considered carefully by Galitzin is the 
effect of frictional resistance on the relative motion of 
earth and boom. However delicately the instrument is 
constructed, there must always be more or less friction ; 



V SEISMOMETRY 69 

and the aim of most constructors has been to minimize the 
friction as far as possible. Milne in his light form of hori- 
zontal pendulum uses the photographic method of taking 
the record ; and in Rebeur-Paschwitz's very delicate 
instrument this method is also employed. What friction 
exists is therefore confined to the pivot or pivots, and to 
the resistance of the air acting on the boom. 

The mechanical method of taking the record by the 
motion of light pointers over a strip of moving paper is 
used by the Italian observers in their vertical pendulums, 
and by Omori in his form of horizontal pendulum. This 
frictional resistance is believed to be practically negligible 
because of the massiveness of the steady body. The 
dynamical theory of the motion of the pendulum (either 
vertical or horizontal) is, however, rendered more com- 
plicated by the fact that the multiplication of the record 
is obtained by having the pendulum in touch with the 
earth at another point in addition to the necessary pivot 
and suspending wire. There is no doubt that Omori has 
with great ingenuity reduced the frictional resistance to 
.a minimum under the conditions. Nevertheless the short 
end of the lever whose longer arm writes out the record 
must act impulsively on the horizontal pendulum ; and 
only a very difficult piece of investigation could show to 
what extent this might influence the steadiness of a deli- 
cately suspended mass with a natural period of one minute. 

It may be of interest to consider the magnitude of the 
force with which the writing lever acts upon the heavy 
body of Omori's horizontal pendulum. A diagram of the 
connexions is shown in Fig. 19. The heavy mass of the 
horizontal pendulum is represented by a circle M , in the 
centre of which is the delicately pivoted pin A which fits 
the fork of the shorter end of the writing lever ABC. The 
axis, B, of the lever is fixed to the earth, and the further 
end C presses on the revolving cylinder with a pressure 
of 5/3 milligrams or fully 1-6 dynes. With coefficient of 
friction 0-6 or 0-7 this will mean a transverse force of 1 or 
1-1 dyne acting at C\ and therefore a push of 10 or 11 
dynes acting at A. 



70 EARTHQUAKE PHENOMENA V 

Suppose now that the boom with the mass M is swinging 
with a period of 60 seconds. The force corresponding to 
displacement x cms. is (27r/60) 2 ra# dynes, where ra is the 
mass in grammes. In Omori's larger form of instrument 
m is about 14 kilogms. or 14,000 grammes. Hence for 
a displacement of 1 mm. or 0-1 cm. the force corresponding 
is 14,000/900 = 16 dynes. Thus it appears that the push 
of the writing lever on the horizontal pendulum is quite 
comparable to the force involved in a displacement of 
one millimetre of the bob of the pendulum from its position 
of equilibrium. 

In the portable form of his horizontal pendulum Omori 
uses a weight of 3 kilogms. with a natural period of oscillation 
of 20 seconds. This means greater stability in the propor- 
tion of about 2 to 1 with a corresponding diminution in 




FIG. 19. 

the relative effect of the frictional resistance due to the 
writing lever. 

In his second memoir on the subject of seismometry 
Galitzin emphasizes strongly the well-known fact that 
under the influence of forced vibrations any system with 
a natural free period of oscillation cannot reproduce in its 
motions these forced vibrations either as regards amplitude 
or phase. He proceeds then to consider the nature of the 
problem when the horizontal pendulum is rendered aperiodic 
by the introduction of a suitable resisting force. This force 
he applies by means of an electromagnetic arrangement. 
Two copper strips are attached symmetrically to the end 
of the horizontal pendulum, one on each side. As the pen- 
dulum moves to and fro relatively to the earth each of 
these copper strips slips through between the poles of an 
electromagnet. This generates induction currents in the 



V SEISMOMETRY 71 

copper strips and these by their reaction upon the magnetic 
field introduce a resisting force the strength of which may 
be varied through a large range by alteration of the strength 
of the electromagnets. The operator has thus the resisting 
force completely under control, and can adjust it so as 
to make the motion of the horizontal pendulum absolutely 
aperiodic. I quote a few sentences from Galitzin's memoir. 

1 The whole investigation shows quite clearly the advan- 
tage of using an aperiodic instead of a periodic instrument. 
The more complicated the true motion of the earth's surface 
the more complicated will be the corresponding seismo- 
gram, and the greater the difficulty of determining the 
march of the function which the displacement is of the 
time. But with a strongly aperiodic instrument the char- 
acter of the seismogram closely approximates to that of 
the earth's motion.' 

The powerful damping of the motion which is needed 
to render it aperiodic has, however, the disadvantage of 
diminishing the amplitude, and the usual methods of 
obtaining a record of weak earthquakes are inapplicable. 
Accordingly Galitzin devised an electric method, in which 
the relative movements of pendulum and earth were trans- 
formed into induction currents in a suitably adjusted coil 
moving with the pendulum. These induced currents were 
then passed through an aperiodic galvanometer, the de- 
flections of which were recorded photographically on moving 
sensitized paper. 

To test the theory as worked out Galitzin used the 
method already referred to of setting the instrument on 
a movable platform and comparing its records with the 
simultaneously recorded motions of the table. It is inter- 
esting to reproduce some of these comparisons. 

The first diagram in Fig. 20 shows the free swing of the 
horizontal pendulum when the table is at rest. The re- 
maining three diagrams and the three diagrams in Fig. 21 
show what occurs when the table is set in simple harmonic 
motion. For ease of reference I shall refer to these by 
number from No. 1 to No. 7 ; and in the following table 
the free swing period, T, of the pendulum during each 



72 



EARTHQUAKE PHENOMENA 



experiment and the period, T', of the imposed swing of the 
table or platform are given in contiguous rows. 



Period 


1 


2 

10-77 
3-57 


Experiment 


7 


3 


4 


5 


6 


T 
T , 


10-77 


10-77 

7-27 


10-6 
5-33 


10-6 
7-06 


8-82 
9-33 


8-82 
irreg. 



Thus in experiment 2 the period of the platform motion 
was 3-57 seconds, while the natural period of swing of the 
horizontal pendulum was 10-77, or just about three times 
as long. The curves show that the pendulum reproduces 




FIG. 20. 

fairly well the motion of the platform ; but there are 
evidences of accumulation of effect due to resonance. In 
experiment 3 the resonance effect is more pronounced, 
because the platform period is nearer in value to the pen- 
dulum period. They are nearly in the ratio of 2 to 3. 
Similar results are shown in experiment 4, in which the 
two periods are nearly as 1 to 2. In all these cases the 
platform curve is recognized by its absolute uniformity. 
On the other hand the motion imposed upon the pendulum 
reproduces the period, but the amplitudes are quite different. 
Consider now experiments 5 and 6 whose curves are 



V SEISMOMETRY 73 

shown in Fig. 21. In the one the ratio of the periods is 
almost exactly as 2 to 3 ; and in the other it is approxi- 
mately as 17 to 18. It will be seen that the resonance is 
very marked. The pendulum still reproduces the period 
of the platform in its swinging ; but the amplitudes pro- 
duced are large, becoming larger the more closely the two 
periods approximate. 

In experiment 7 we see the effect of an irregular and 
not even approximately periodic motion of the platform. 
As in the other cases the instrument begins with the same 
kind of movement as the platform, but because of the 




FIG. 21. 

initial effect of a suitable succession of impulses it speedily 
acquires its own proper swinging motion, on which are 
superposed irregularities corresponding roughly with the 
irregular jerks of the platform. A slightly different suc- 
cession of impulses at the beginning would no doubt have 
produced a very different amount of natural swing. It 
would be impossible to say beforehand what effect a par- 
ticular succession of irregular impulses might produce. 

We shall see below that the essential features of the 
seismograms of these artificial earthquakes are all to be 
met with in records of real earthquakes. 



74 EARTHQUAKE PHENOMENA V 

We pass now to the next set of curves shown in Fig. 22. 
These indicate the results obtained from experiments with 
the same instrument when its periodic oscillations are 
destroyed by means of sufficiently powerful damping. In 
other words the instrument is in an aperiodic state. The 
first three diagrams in the figure show the response of the 
aperiodic seismometer to sinusoidal movements of the 
platform with three different periods. The instrument 
curve begins on the left a shade later than the platform 
curve and indicates a certain irregularity for the first period. 
Thereafter the one curve is almost an exact copy of the 




FIG. 22. 

other, differing in phase and slightly in amplitude. In the 
last diagram of Fig. 22 we have an example of the manner 
in which an irregular disturbance of the platform is imitated 
on the seismometer. The platform curve may be easily 
distinguished as that in which there are straight line gaps 
during which the platform was at rest. During this resting 
stage the horizontal pendulum is seen to swing slowly and 
aperiodically from the displacement it happened to have 
towards its position of equilibrium. There is a correspon- 
dence between the succession of crests and troughs in 
the two curves, but there is not strict identity. Both in 
amplitude and phase there are considerable deviations. 



V SEISMOMETRY 75 

Nevertheless there is no doubt that the aperiodic instrument 
reproduces something like the motion of the platform ; 
whereas the periodic seismometer is absolutely untrust- 
worthy in this respect, except for vibratory motions whose 
periods are distinctly smaller than the free period of the 
pendulum. 

We may therefore conclude that in seismometers in which 
the frictional restraints have been reduced to a minimum 
only the more rapid movements of earth are approximately 
reproduced. When the frictional restraints are consider- 
able, as they certainly are in the earlier types of pendulum 
bracket seismographs used by Ewing, Gray, and Milne, the 
record may not be very far from being a fairly faithful 
reproduction of the earthquake motion, indicating at all 
events the broad succession of motions and impulses. But 
in no case can we regard them as absolutely trustworthy 
in a truly quantitative sense. 

In the analysis given above of the kinds of motion to 
which a horizontal pendulum would be sensitive a dis- 
tinction was drawn between horizontal motion and tilting. 
It is difficult, as Milne has pointed out, to accept the fact 
of vertical motion and not at the same time to admit the 
existence of tilting. A measurable amount of tilting means 
a wave passing with a definite velocity over the surface of 
the ground. The maximum tilt associated with such 
a wave may not of course make itself wholly felt on the 
horizontal pendulum. The action is a kinetic, not a static 
one. And unless the period of the wave approximates to 
the period of free vibration of the pendulum the forced 
oscillation may have an amplitude smaller than the dis- 
placement which would be caused by a steady sustained 
tilt of the same amount. It is obvious, in fact, that a very 
rapid wave motion accompanied by tilting will have very 
little effect indeed upon the delicately poised horizontal 
pendulum, for the same reason that an ordinary galvano- 
meter included in the secondary circuit of a rapidly working 
induction coil shows nothing but a quivering motion about 
its zero position. 

Again, as clearly established by Galitzin, it is impossible 



76 EARTHQUAKE PHENOMENA V 

to separate dynamically the effects of the tilting from the 
effects of the horizontal acceleration. 

Bearing these considerations in mind we cannot accept 
what at first sight may appear to be negative evidence as 
really disproving the existence of tilting. For example, 
Omori describes certain experiments with a set of hori- 
zontal pendulums, from which he concludes that in the 
ordinary moderate earthquakes which visit Tokyo there is 
no tilting. Two horizontal pendulums are set up side by 
side practically identical in all respects, except that the 
stability angle i, which is believed to determine the sensi- 
tiveness of the instrument, has different values in the differ- 
ent instruments. The smaller the stability angle i which 
the vertical line makes with the line about which the hori- 
zontal pendulum swings, the less stable is the instrument, 
and the greater the deviation of the boom from its equi- 
librium position when a given constant tilt is imposed on the 
instrument about this equilibrium position. The argument 
is that if tilting be present to any appreciable extent the 
records of any earthquake obtained on the different pen- 
dulums will have markedly different amplitudes, the more 
sensitive giving the greater amplitude because of its in- 
creased response to the tilting action. The point is of 
some importance and calls for a detailed discussion. To 
make it quite intelligible to those whose mathematical 
knowledge is limited, I shall give the numerical details of 
four cases. 1 

The equation of motion of a body oscillating through 
small ranges about a position of equilibrium is 

x + 2kx + ri*x = 0, 

where x is the acceleration due to the force of restitution 
urging the body back to the equilibrium position when its 
displacement from that position is x, where 2&# is the 
acceleration due to resistances proportional to the speed #, 
and where n is a number proportional to the frequency of 

1 Wiechert in his Tfieorie der automatischen Seismographen ( Abh. d. Kon. 
Ges. d. Wissen. zu Gottingen) gives a similar discussion, but not for quite 
the same object. 



V SEISMOMETRY 77 

the unresisted vibration, being equal to the ratio of 2-rr 
to the periodic time. When k is numerically smaller than n 
the body has an oscillatory motion of period 2ir/ \/(n 2 fc 2 ). 
But when k is the greater quantity there is no oscilla- 
tion, the motion is aperiodic. The body when displaced 
from its position of equilibrium slowly settles back 
towards the equilibrium position, but does not oscillate to 
and fro about it. This aperiodic motion is produced 
evidently by making k large enough. When k is not too 
large, the motion is periodic. Under the influence of the 
frictional forces, the amplitude of the free vibrations will 
gradually diminish as time goes on, and unless the body 
receives a fresh impulse will ultimately decay completely. 
So much for the free vibration. 

But now suppose the body to be acted on by an external 
rhythmic force such as would come into play if a suitable 
tilting of the ground took place below a horizontal pen- 
dulum. It is usual to represent this forced vibration by 
an expression of the form/ cos #>, where 2ir/p is the periodic 
time of this sinusoidal forced vibration. The equation of 
motion then becomes 

x + 2ka + n 2 x = f cos pt, 

and the complete solution consists of a free vibration 
portion which decays in time and a forced vibration portion 
which persists so long as the forcing vibration continues 
to act. Ultimately this part is the more important ; and 
its amplitude is measured by the expression 



In the horizontal pendulum the quantity n 2 = gi/l, where 
i is the inclination to the vertical of the axis about which 
the pendulum rotates, g is the acceleration due to gravity., 
and I is the effective length of the boom and attached 
heavy body. This expression shows that the sensitiveness 
increases as the angle i diminishes ; and it can also be 
easily shown that the deviation of the pendulum from its 
natural position of equilibrium when the instrument is 



78 EARTHQUAKE PHENOMENA V 

tilted through a small angle $ is equal to the ratio $/i. 
Thus the smaller i for a given tilt the greater the statical 
deviation. 

But a consideration of the above expression for the 
amplitude when the tilting takes place with a rhythmic 
variation shows that there is no such simple relation be- 
tween deviation and tilt at any given instant as might be 
expected from consideration of the statical effect only. 
For example, when p is large compared to n y that is, when 
the forced vibration is quicker than the free vibration of 
the instrument, the term (1 n 2 /p 2 ) differs very little from 
unity, and the effect of n 2 is practically negligible. In other 
words we may increase n from any small fraction of a given 
p up to 1/3 of p, and the change in the amplitude will not 
thereby be affected by more than 10 or 12 per cent. But 
it is through n 2 , which is proportional to the stability angle i, 
that the sensitiveness of the horizontal pendulum is be- 
lieved to come into account. So long then as we are deal- 
ing with forced vibrations whose periods are less than one- 
half of the period of free vibration of the pendulum, we 
may vary the latter by varying i through a wide range and 
not appreciably affect the amplitude of the motion imposed 
upon the pendulum. 

To bring out the point quite clearly and at the same 
time to show how the value of k influences the numerical 
details, I have calculated the relative values of the ampli- 
tudes for different ratios n/p and for four different values 
of k/n. The results are shown in the following table. The 
first column contains the values of n 2 /p 2 , which for a given 
value of p may be taken as proportional to the stability 
angle i, and therefore as inversely proportional to what is 
usually called the sensitiveness to tilting of the horizontal 
pendulum. The four following columns contain the values 
of the amplitudes of the vibration forced upon the hori- 
zontal pendulum in virtue of a periodic tilting movement 
of period 2-rr/p about the direction of the boom as axis. 
These are tabulated under headings which give the assumed 
values of k 2 /n 2 . 



V 



SEISMOMETRY 

FORCED VIBRATION AMPLITUDES FOB VARIOUS VALUES OF THE 
PERIOD AND THE RESISTANCE. 



79 



nVp 2 


k*/n? = 


Static 
Sensitiveness 


1/400 


1/40 


1/4 


1 


0-01 


1 


1-004 


1-005 


0-99 


100 


04 


1-04 


1-04 


1-02 


96 


25 


16 


1-19 


1-18 


1-08 


86 


6-25 


36 


1-56 


1-5 


1-14 


74 


2-78 


64 


2-71 


2-27 


1-15 


61 


1-56 


81 


4-76 


2-92 


1-09 


55 


1-24 


1 


10 


3-16 


1 


50 


1 


1-21 


4-22 


2-46 


0-89 


45 


83 


1-44 


2-19 


1-72 


81 


41 


69 


2-25 


0-79 


0-75 


51 


31 


44 


4 


0-33 


33 


28 


20 


25 


9 


12 


12 


117 


10 


11 



The last column of numbers gives the reciprocals of the 
quantities n 2 /p 2 and shows what the relative deviations 
would have been had the statical law held. It is abundantly 
evident that the estimated sensitiveness of horizontal 
pendulums in terms of the time of free swing has absolutely 
no applicability to the practical case of the recording of 
earthquake motions. The significance of these calculations 
is shown clearly in their graphical representation (Fig. 23). 
The quantities n 2 /p* are measured horizontally, and the 
corresponding amplitudes vertically. If we suppose p to 
be constant the abscissae will vary as n z , becoming greater 
as the free swing period becomes less. This is the point of 
view to be taken when we are considering how the kinetic 
sensitiveness of the instrument depends on the stability 
angle i. Again, if we suppose n to be constant, the 
abscissae will increase as p diminishes, that is, the abscissae 
will vary directly as the square of the period of the forced 
vibration. This is the usual way of regarding the facts 
represented by the graphs. Taking the former point of 
view and regarding p as constant, we see that the abscissae 
will be for the same instrument directly proportional to 
the stability angle i, so long as that angle remains small. 
The abscissae are therefore inversely proportional to the 
static sensitiveness, and this is shown by the dotted curve, 



80 



EARTHQUAKE PHENOMENA 



V 



which is simply the last column of numbers plotted against 
the first. It is of course a rectangular hyperbola. 

The full line curves represent the kinetic cases. For very 
slow periodic variations of the external force the kinetic 
case approaches the static case ; for high values of n z /p- 
the curves tend to coalescence. But as the period of the 
forced vibration is diminished towards equality with the 
natural period of swing of the pendulum the kinetic curves 




begin to deviate perceptibly from the static curve. In the 
two cases in which the frictional resistances are not large 
this deviation is very marked, and the sensitiveness of the 
instrument increases rapidly with the free swing period ; 
but this increase ceases and the amplitude reaches a maxi- 
mum when n equals p, that is, when the forced vibration 
is isochronous with the free swing of the pendulum. Now 
in all practical cases the inventors have for good reasons 



V SEISMOMETRY 81 

increased the period of the instrument as much as possible, 
retaining just sufficient stability to enable the horizontal 
pendulum to keep a steady position of equilibrium. Con- 
sequently the periods of the earthquake motions which 
have been found to occur in most cases are generally less 
and often very much less than the periods of free swing of 
the instrument. Thus in Omori's most delicate type of 
horizontal pendulum the free swing has a period of more 
than 60 seconds, whereas earthquake motions rarely exceed 
the half minute in period, and most of the periods are 
much smaller, such as 4, 8, 11, &c. In the bracket seismo- 
graphs of Ewing, Gray, and Milne, the free swing period 
may be from 2 to 4 seconds ; but in these the frictional 
resistances are considerable, and may prevent excessive 
resonance effects. In general, the longer the period in slow 
swinging instruments, the less prominent will resonance 
effects be ; for there is less chance of the forced and free 
vibration periods being equal. 

Professor Dyson and Mr. Heath have supplied me with 
data from which the necessary constants for the Milne 
horizontal pendulum installed at Edinburgh may be cal- 
culated. The natural period of swing was 15-3 seconds ; 
and from a beautiful photographic record of the decaying 
motion when the instrument was deflected and then left 
to itself I was able to calculate the logarithmic decrement 
and from that determine the ratio k 2 /n 2 . Thus the ranges 
of motion for successive to-and-fro swings in the period 
15-3 seconds were 9-6, 7-4, 6-15, 5-05. The ratios of the 
successive pairs are 1-3, 1-2, 1-23, which are as consistent 
as the method of measurement will allow. Taking the 
mean as 1-25 we find for the ratio k 2 /n 2 almost exactly 
1/800. By another method of measuring I found that the 
amplitude was diminished to one half in a distance of 
1 mm. on the record. But 59 mm. correspond to 1 minute ; 
hence working out by means of this relation I determined 
the ratio of k 2 /n 2 to be 1/1300. It is not certain that at 
the time the record of the decaying motion was taken the 
period was exactly as stated ; and in any case the smallness 
of the record prevents any great precision in the measure- 



82 EARTHQUAKE PHENOMENA V 

ments either of time or amplitude. We shall not be far 
wrong if we take 1/1000 to be about the value of the ratio 
of P/7i 2 for the particular seismometer in use in the Edin- 
burgh Royal Observatory. A consideration of the expres- 
sion above shows that except in the immediate vicinity 
of p = n the effect of taking k*/n 2 smaller than 1/400 is of 
no great consequence. 

I have no information as to the relative magnitudes of 
the frictional resistances in other cases, although they 
could be easily obtained by noting the rate of decay of the 
free swing. Provisionally we may take the first case 
(n a = 400& 2 ) as corresponding to Omori's horizontal pendulum, 
and the second case (n 2 = 40& 2 ) as corresponding to the more 
stable type of bracket seismograph. In both cases in 
accordance with the law of resonance a maximum is reached 
when the free and forced vibrations have equal periods ; and 
the sensitiveness in the neighbourhood of this condition is 
greater than would be expected from the statical law. 
But thereafter as the period of the forced vibration is 
diminished, or as the period of the free vibration is increased, 
the amplitude falls off towards a definite value for excessively 
rapid forced vibrations or for extremely long free vibration 
periods. The law of change of sensitiveness as estimated 
by the amplitude imposed upon the instrumental record 
and there is no other real way of estimating sensitiveness 
follows a law entirely different from that which the statical 
relation between deviation and tilt would suggest. The 
sensitiveness in the kinetic cases diminishes when it ought 
to increase according to the static law. In the third curve, 
which represents a case of great frictional resistance but 
not quite great enough to destroy periodic motion of the 
pendulum, the law of sensitiveness follows the static law 
very closely up to the critical condition n 2 =p*', but for 
smaller values of the ratio n z /p 2 there is hardly any appre- 
ciable change.^ Finally, for the limiting aperiodic case the 
sensitiveness increases steadily but slowly all the way as 
n 2 /p 2 diminishes towards zero. It is easily seen from the 
formula that A is inversely as (l + n 2 /> 2 ), so that there is 
no critical condition given when n = p. 



V SEISMOMETRY 83 

In this discussion I have assumed the usual results of 
forced vibrations acting upon a vibrating system with 
a certain amount of frictional resistance present. But 
Oalitzin's curves show that this theory is incomplete. 
Theoretically the free vibration which may be started at 
the beginning is regarded as decaying in time so as to 
become comparatively unimportant, while the forced 
vibration is sustained. This solution might be called the 
kinematic solution of the problem ; but dynamically it 
is incomplete. There seems to be little doubt that the 
free vibration is always being started anew by appropriate 
impulses from the forced vibration. If the action of the 
forced vibration were to cease at any instant the system 
would continue to swing to and fro with the free-swing 
period. This tendency to start free vibrations is always 
present ; and will be aided or thwarted according to the 
momentary phase of the forced vibration. The net result 
seems to be that although the free vibration may not always 
show itself distinctly it is always present in an incipient 
state. There will consequently be interference effects 
between the forced vibration imposed on the system and 
the more or less incipient free vibration which may be 
said to be potentially present. 

This discussion proves four points of some importance. 

(1) The amplitudes of records obtained on delicate 
seismometers in which frictional resistances have been 
reduced as much as possible have no simple relation to what 
might be called the statically estimated sensitiveness of 
the instrument. The amplitudes depend far more upon 
the relative amounts of friction present and upon the 
numerical relation between the periods of the forced earth- 
quake vibrations and the free-swing period of the instrument. 

(2) The conclusion that tilting in earthquake movements 
is disproved by the fact that two seismometers of different 
sensitiveness as estimated statically do not give propor- 
tionally different amplitudes in their records of the same 
earthquake is dynamically unsound. 

(3) When with a horizontal pendulum swinging fairly 
freely the period of the earthquake motion approaches 

G2 



84 EARTHQUAKE PHENOMENA V 

within, say, 30 per cent, of the period of free swing of the 
pendulum, the amplitude of the record is in virtue of the 
law of resonance greatly increased. In such cases, and 
they are of frequent occurrence, the recorded amplitudes 
give no real measure of the earthquake amplitudes. This is 
beautifully illustrated by Galitzin's curves. 

(4) Even when the pendulum is made aperiodic, the only 
condition in which according to Galitzin's investigations 
anything like a faithful reproduction of the earth's motion 
is possible for all periods, the increase of the static sensi- 
tiveness does not greatly increase the kinetic sensitiveness. 

Bearing in mind these conclusions we are ready to con- 
sider the significance of the records which have been obtained 
on seismometers and seismographs of various kinds. 

First, as regards the evidence of pronounced resonance, 
I shall quote from a letter which I sent to Nature (vol. xli, 
p. 32) in reference to the earthquake which occurred in 
Tokyo on April 18, 1889. 

' It was my good fortune on the day in question to be 
engaged in conversation with Professor Sekiya in the 
Seismological Laboratory (of the Imperial University of 
Japan) at the very instant the earthquake occurred. We 
at once rushed to the room where the self-recording instru- 
ments lay, and there, for the first time in our experience, 
had the delight of viewing the pointers mark out their 
sinuous curves on the revolving plates and cylinders. At 
first sight it seemed as if the pointers had gone mad, tracing 
out sinuosities of amplitude five or six times greater than 
the greatest that had ever before been recorded in Tokyo. 
There was not much sensation of an earthquake ; indeed, 
after the first slight tremor that attracted our attention, we 
felt nothing at all, although in the irregular oscillations 
of the seismograph pointers we had evidence enough that 
an earthquake was passing. Very few in Tokyo were 
aware that there had been an earthquake until they read 
the report of it in next day's papers.' 

A similar experience is thus described by Milne in the 
account of what he observed in Tokyo on the morning of 
October 28, 1891, when the great Mino-Owari earthquake 
wrought such havoc in central Japan : 

' From the manner in which my house was creaking 



V SEISMOMETRY 85 

and the pictures swinging and flapping on the wall I knew 
the motion was large. My first thoughts were to see the 
seismographs at work ; so I went to the earthquake room, 
wliere to steady myself I leaned against the side of the 
stone table, and for about two minutes watched the move- 
ments of the instruments. It was clear that the heavy 
masses suspended as horizontal pendulums were not behav- 
ing as steady points, but that they were tilted first to the 
right and then to the left . . . That whenever vertical 
motion is recorded there must be tilting and therefore no 
form of horizontal pendulum is likely to record horizontal 
motion, is a view I have often expressed. What I then 
saw convinced me that such views were correct.' 

So far I agree with Milne that vertical motion implies 
tilting ; but I am not so sure that tilting is, except in certain 
extreme cases, so conspicuous as to mask the effects of 
to-and-fro horizontal motion. As Galitzin has shown, no 
horizontal pendulum can separate out the effects of tilting 
and of horizontal motion. But we do not require to invoke 
the existence of tilting to explain these great excursions 
of the seismograph pointers. Pronounced resonance effects 
will exist when the earthquake motion is fairly rhythmic 
with a period not very different from the period of free 
swing of the seismometer. In the earthquakes just 
described there were periodic motions which fairly well syn- 
chronized with the free-swing period of the instrument. 
In the earthquake of April 18, 1889, the motion was com- 
paratively gentle with a long period of several seconds. 
In the earthquake of October 28, 1891, on the other hand, 
there was mingled with the slower periodic motions, as 
experienced at Tokyo, an alarming amount of rapid oscilla- 
tions. The position of the epicentre of the latter earth- 
quake was known only too well ; but it was not possible 
to locate the origin of the earlier shock with any precision. 
Probably it had its source below the waters of the Pacific 
Ocean to the south or south-east of Tokyo. The shock of 
April, 1889, is, however, of special historic interest, as being 
the first earthquake which was recognized as having pro- 
duced a characteristic effect on the delicate horizontal 
pendulums installed by Rebeur-Paschwitz at Potsdam and 
Wilhelmshaven. See below, chapter xi. 



86 EARTHQUAKE PHENOMENA V 

It is interesting to compare seismograms which the same 




I I 



instrument gives of different earthquakes. In Fig. 24 



V SEISMOMETRY 87 

I have reproduced on a reduced scale of 4 to 11 three sets 
of diagrams obtained with an early form of the Gray-Milne 
seismograph. The middle set contains the three com- 
ponent seismograms of the earthquake of April 18, 1889, 
already described, while the other two sets show the same 
elements for other earthquakes which occurred the same 
year. In all the vertical motion is small ; and although 
it may reach a larger amplitude in the last of the three, yet 
it is on the whole more pronounced in the other two. There 
is not, however, much to choose between the vertical seismo- 
grams of the first and second, unless it be that there is in 
the latter a clearer indication of long oscillations of periods of 
from 3 to 4 seconds. It is in the horizontal seismograms 
that the startling difference is shown. The conclusion 
seems to be obvious. In the April earthquake record we 
are face to face with a real resonance effect, the period of 
the motion of the ground being sufficiently in tune with the 
natural time of oscillation of the horizontal pendulums to 
start it swinging with that period. For if it were simply 
a question of tilting, and if tilting be a necessary concomitant 
of vertical motion, we should have expected the horizontal 
seismograms of the March earthquake to show as large 
amplitudes as those of the April shock. There is no doubt 
at any rate that the character of the horizontal seismograms 
is entirely changed when we pass from the records for the 
April earthquake to those of the other two. 

In the later forms of the Gray-Milne seismometer the 
records are traced on a strip of paper drawn over the cylinder 
at a steady rate which is suddenly accelerated when the 
earthquake begins. In Fig. 25 a portion of a set of seismo- 
grams is shown, reduced in the ratio of 10 to 22 from the 
diagram in Baron Kikuchi's account of recent seismological 
investigations in Japan. This indicates in my opinion in 
an unmistakable manner the effect of resonance upon the 
character of the record. The portions shown are for an 
interval of fully twenty seconds. In the early part of each 
seismogram rapid vibrations are evident especially in the 
vertical component. Very soon, however, a comparatively 
long period oscillation begins to appear in the East-West 



88 



EARTHQUAKE PHENOMENA 



seismogram. On this the rapid corrugations are super- 
posed. In the fourth second this seismogram breaks off 
but begins again in the eighth second, and after ten seconds 



! I 

i' 



ii 



H -i 

i 1 




FIG. 25. 



makes several large oscillations in which the rapid corruga- 
tions are visible only at the crests and troughs, being quite 
masked when the movement is swift from side to side. 



V SEISMOMETRY 89 

Similar oscillations, not so strongly marked, are seen on 
the north-south and on the vertical motion seismograms. 

There seems to be little doubt that we are dealing here 
with instrumental peculiarities and not with true measure- 
ments of surface motions. The periods of the earthquake 
motions are probably fairly well indicated ; but not the 
amplitudes. This indeed is impossible with free-swinging 
horizontal pendulums, except for very rapid oscillations, 
such as generally show themselves at the beginning of 
a shock. As illustrated by the third curve in Fig. 22 an 
arbitrary impulse may start the pendulum moving with its 
own period, and on these larger movements of the seismo- 
graph rapid oscillations are frequently superposed. These 
we may regard as true earthquake movements ; but we 
cannot in the light of the preceding discussion consider the 
large excursions of the recording pointers as reproducing 
the real motion of the ground. 

The elimination of periodicity in a seismometer must be 
accomplished by the introduction of a suitable ' damping ' 
arrangement under complete control, either electromag- 
netically (after Galitzin) or by pistons working in perforated 
cylinders through which air can pass, as in Wiechert's forms 
of instrument. An accurate reproduction of the motion 
of the ground is possible only when the aperiodic condition 
is fulfilled ; but this is difficult to realize practically because 
of the accompanying diminution of amplitude. Even with 
Wiechert's so-called astatic instruments and others of 
modern construction provided with a controllable damping 
arrangement there is still periodicity, and the records show 
resonance effects similar to those we have just been dis- 
cussing. Nevertheless suitable damping diminishes the 
magnitude of the resonance effect and improves the action 
of the seismograph. 



CHAPTER VI 

EARTHQUAKE DISTRIBUTION 

Seismic and Aseismic Regions. Definition of Seismicity. Survey of 
Limited Areas. Milne's Survey of Tokyo. Earthquake Catalogues. 
De Ballore's Methods. Rudolph's Analysis of Sea-quakes. Milne's 
Chart of Large Earthquakes. De Ballore's Criticisms. 

IT has long been recognized that certain regions of the 
earth's surface are peculiarly subject to earthquakes ; and 
that in certain other districts earthquakes rarely if ever 
happen. Between these extremes there are all possible 
degrees of earthquake visitation. 

It may be laid down as a general rule, that where small 
and moderate seismic shocks are frequent, destructive 
earthquakes are more familiar than in regions not subject 
to frequent shakings. There are of course exceptions, such 
as at Comrie in Scotland, where no destructive shock has 
happened in historic times, or at Lisbon, famous in history 
because of the great earthquake of Nov. 1, 1755, and yet 
not a place of seismic importance in the ordinary sense 
of the term. Nevertheless it is generally true that destruc- 
tive earthquakes visit at intervals regions which are charac- 
terized by great frequency of slight or moderate shocks. 

We may use the term seismic frequency as an indication 
of the degree to which a given region is subject to earth 
shakings. We may suppose the number of individual 
shocks to be known as having occurred over a limited area 
in a given number of years. The ratio of these two numbers 
will give an average annual seismic frequency for that region 
during that time. The greater the number of years taken 
into account, and the more care in noting and recording 
the shocks, the better will be the approximation to the 
estimate of the seismic frequency. Unfortunately the 
regular recording of small shocks is comparatively recent, 
so that statistics for great stretches of the earth's surface 
are necessarily far from complete. As an illustration take 



VI EARTHQUAKE DISTRIBUTION 91 

the case of Japan. We may suppose the number of earth- 
quakes recorded, say, in twenty years to be divided by 20, 
giving a good annual mean. Then, dividing this annual 
mean by the area of the country, we get the mean annual 
frequency per unit area. Let us call this the seismicity of 
the country. Now, there are many districts in Japan 
which are hardly ever visited by perceptible shocks ; and 
the vast majority of recorded earthquakes occur in a few 
limited districts. It is clear then that the seismicity esti- 
mated as above for the whole country must be smaller, 
probably much smaller, than the true seismicity of any one 
of these limited regions. Indeed just as we recognize, 
broadly speaking, certain countries as of seismic character, 
so in any one of these countries we recognize great differ- 
ences in the earthquake frequencies characterizing different 
parts of the country. Milne in his catalogue of 8,331 earth- 
quakes which happened in Japan between the years 1886 
and 1892 concludes that there are fifteen distinct districts 
susceptible to seismic effects ; and that outside these the 
rest of Japan is practically quiescent. 

Not only so, but in the limited region of the city of Tokyo 
the susceptibility to earthquake shocks varies greatly with 
locality. This question was investigated in 1887-8 by 
Milne by means of a system of postcards distributed to 
fully 100 observers resident in different parts of the city. 
When a shock was felt the observer filled in the information 
on a postcard and returned it to Professor Milne. During 
the six months from November 15 to May 5, 496 records 
from 103 observers were sent in. Of these 370 came from 
61 observers living on high ground in the west and north of 
Tokyo ; and 126 from 42 observers living on low ground. 
Note that we are dealing with the susceptibility of observers 
to earthquake shocks, not with instrumental records of 
earthquakes. The distinction is important and should be 
borne in mind in all questions based on the statistics of 
earthquakes felt or recorded by man. 

It would thus appear that in Tokyo more shocks are 
felt by observers on high than by observers on low ground- 
about twice as many, indeed. The reason of this is to be 



92 EARTHQUAKE PHENOMENA VI 

found in the following further facts. The records had to do 
with 69 distinct earthquakes. Of these 36 were felt over 
a wide area outside Tokyo ; but of these only 6 were 
felt all over Tokyo. The remaining 33 were felt on the 
high hilly ground only. An examination of the periods 
of vibration of these various shocks as recorded on the 
instruments in Tokyo gave an average period of 0-76 for 
the 6 felt all over Tokyo, and 1-85 for the 30 felt only on 
the high ground. Thus it would seem that for a moderate 
shock to be felt by an observer on low alluvial ground, 
a quicker vibration is necessary than when the observer 
is on high hilly ground. In connexion with this it is well 
also to mention that the instrumental record shows in 
general a larger slower motion on the low alluvium than 
on the rocky ridge. It is apparent, in fact, that extent of 
movement does not entirely determine susceptibility to an 
earthquake. The rapidity of the vibration is also an 
important factor. The hearing of earthquake sounds with- 
out the sensation of movement is, in fact, simply a limiting 
case, the vibration being very short in period but small in 
amplitude. 

The early catalogues of earthquakes prepared by Mallet, 
Perrey and others, though necessarily incomplete, indicated 
the broad features of seismic distribution over the surface 
of the earth ; and within recent years the industry of 
M. de Montessus de Ballore has given a greater certainty 
to the conclusions which had been indicated if not expressly 
formulated. De Ballore has published his own views in an 
important work, Les Tremblements de Terre, Geographic 
seismologique, which is essentially a detailed account of all 
the earthquake regions of our globe. 

Some years ago de Ballore introduced a method of 
measuring seismicity, practically identical with the method 
of finding the average annual frequency of shocks per unit 
area. In the book just published he has definitely given 
up this method on the ground that earthquakes are dis- 
continuous phenomena, so that all attempts to represent 
seismic distribution over the world by means of continuous 
seismic lines or shaded areas rest on a false and unscientific 



VI EARTHQUAKE DISTRIBUTION 93 

basis. He has accordingly used in his book a discontinuous 
method of indicating seismic frequency. A small black 
disk is set over each locality, the radius of the disk indicat- 
ing on a purely conventional scale the average annual seismic 
frequency. The appearance of his charts is very striking, 
and the eye is able to pick out at once the places of greatest 
seismicity. Probably the method is as good as any other 
in the case of districts only moderately subject to seismic 
disturbances. But in countries like Italy and Japan where 
shocks are numerous there is not the same difficulty in 
drawing lines of equal seismicity with fair accuracy. 

The accuracy of earthquake statistics must depend 
ultimately upon the amount of the earth's surface inhabited 
by civilized man. There are many large tracts of land 
destitute of inhabitants, or inhabited by nomadic or semi- 
barbarian races. Any shocks occurring there are not re- 
corded, unless they happen to be very severe ones which 
cause terror and panic. 

Again, the land surface of the globe is only a fraction 
of the whole surface ; and it is obvious that many earth- 
quakes originating below the sea will be unfelt by dwellers 
on the nearest land. As a matter of fact we know that 
a large percentage of shocks which are felt have their source 
beneath the neighbouring bed of ocean. For example, 
almost all the moderate quakes in the Tokyo- Yokohama 
district of Japan originate in the Pacific ocean to the south 
and east. This no doubt is why they are as a rule so 
moderate in their intensity. It is clear then that an earth- 
quake statistic based wholly on felt shocks cannot but be 
incomplete. 

This incompleteness has been partially filled in by 
Rudolph's tabulation of the so-called sea-quakes ; but 
still more effectively by Milne's recent charts of large 
earthquakes ' which shake the whole earth'. 

The sea-quakes tabulated and discussed by Rudolph 
differ from ordinary earthquakes only in the fact that their 
origins have been below the ocean, and that generally they 
have not been powerful enough to make themselves felt in 
the nearest countries. The disturbance produced over 



94 EARTHQUAKE PHENOMENA VI 

a limited region of the ocean bed has caused condensational 
waves to pass upward through the water. These have been 
felt and heard by passing vessels ; and it is from the logs 
of the captains that Rudolph drew his information. It is 
obvious, however, that the record of shocks felt by ships 
at sea must be far more incomplete than the records of 
shocks on land. The ships are comparatively few in number 
compared to the great stretches of ocean over which they 
navigate. Moreover the routes are mainly determined by 
commercial considerations ; and large parts of the sea are 
rarely if ever visited. Very many suboceanic shocks must 
escape detection. 

The nature of the shock experienced on board ship is 
best indicated by quotation from some of the logs collected 
and discussed by Rudolph. 

' 9 June, 1882. Capt. Stiven of the Arethusa, 32 41' N., 
39 50' W. Experienced sharp shock of earthquake. It 
shook the ship so violently from stem to stern that all 
hands came running out to see what was the matter. I was 
standing on the poop at the time and the vibration seemed 
vertical. The wheel was shaken in the helmsman's hands. 
It was accompanied by a rumbling noise like distant thunder, 
but seemed close to us. It was something like a heavy 
cask being rolled quickly along the deck from forward, 
and in fact I thought at first it was so, but a moment's 
consideration showed it could not be, the ship shaking far 
too much for that . . . The phenomenon lasted for say 
10 seconds.' (Rudolph estimates intensity at VII.) 

' 22 Dec., 1884. The Azores. Capt. Balderston of the 
Belfast, 34 34' N., 19 19' W. The ship was shaken by an 
earthquake which lasted from about 75 to 90 seconds. The 
shaking was accompanied by a loud rumbling noise which 
as heard from the cabin resembled the sound which would 
be made by the rolling of large empty or iron tanks about 
the decks ; but which as heard from the upper deck and 
in the open air was as that of not very distant thunder, 
and it appeared to fill the whole air ... I cannot say in 
what compass bearing of the visible sky it commenced, but 
it travelled rapidly through the air towards the S.W. . . . 
The helmsman found the steering wheel much shaken as 
he held it, and in the cabins and cookhouse tin ware, crockery 
ware, and other light articles were rattled about . . .' (Esti- 
mated intensity VI.) 



VI EARTHQUAKE DISTRIBUTION 95 

' 9 May, 1877. St. Paul's Islands. Capt. Murdoch of 
the Denbighshire, 52' N., 28 IS' W. Two severe shocks 
of earthquakes : the first shock was like a jarring of every- 
thing in the ship. On deck it appeared as if the chain 
cables were running out and the topmast yards coming 
down by the run, and it seemed as if at every step we took 
on deck we must fall down : this shock lasted 30 or 40 
seconds. The water was not at all agitated nor phos- 
phorescent, the weather was rather sultry and hot below, 
so that I had been on deck most of the watch with the 
mate. After the first shock was over I told the carpenter 
to sound the pumps. All hands had rushed on deck, 
thinking the ship was on shore, and while sounding the 
pump the second shock occurred. It was sharp and instan- 
taneous, as if a large cannon had been fired immediately 
below the ship. There was no mistaking this last ; it was 
a volcanic eruption or explosion. The noise that accom- 
panied the first shock was like the low groaning of distant 
thunder, but yet it appeared near and about us. The 
sensation and noise during the first shock was most peculiar. 
I tried the temperature and specific gravity immediately 
after the second shock, but there was no apparent change.' 
(Estimated intensity VII.) 

There is no mistake as to the general nature of these 
experiences, and the explanation of all the phenomena is 
simple enough. As pointed out in chapter x below, 
a disturbance originating below the bed of the ocean will, 
whatever may be the angle of incidence within the rock, 
proceed through the water as a compressional wave in 
a direction almost perpendicular to the general lie of the 
ocean bed. This is because the speed of propagation of 
the condensational wave in water is much smaller than 
the speed of propagation of the elastic waves in the rock. 
For the same reason a second refraction at the upper surface 
of the water into the air will give rise to waves of condensa- 
tion in the air passing upwards in a direction almost truly 
vertical. These compressional waves, if of sufficiently short 
period, will produce sound. The hearer will hear this sound 
as being all around him, emerging as it does almost verti- 
cally. He will not hear it first as coming from any direc- 
tion, but he may hear it in the later stages coming from 
the direction in which the later disturbances are passing 



96 



EARTHQUAKE PHENOMENA 



VI 



away through the water, that is, in the direction opposite 
to that from which the disturbance originally came. The 
shaking of the ship from stem to stern and the jarring of 
everything in the ship are just what a complex succession 
of variations of pressure in the water would produce through 
the solid and almost rigid body of the ship. 

The general results of Rudolph's investigation are given in 
the following table of sea-quakes from 1720 to 1886. 



SEA 

N. Atlantic 

Eq. Atlantic 

S. Atlantic 

W. Indies, Caribbean 

Mediterranean 

Indian Ocean 

E. of N. Pacific 

W. of N. Pacific 

E. of S. Pacific 

W. of S. Pacific 

E. Indies . 

Total . 



Sea 



NUMBER OF SHOCKS 

52 
65 
10 
34 
31 
28 
22 
14 
47 
10 
20 

333 



Remembering that there must be a tendency for more 
earthquakes to be observed in this way in regions frequented 
by ships than in regions hardly ever visited, we must con- 
clude that the numbers are too few to serve as a basis for 
sure argument, with perhaps two exceptions. These are 
the equatorial Atlantic and the East of the South Pacific. 
The shocks felt in these seas are so numerous compared 
with the shocks felt in more frequented seas that we may 
safely regard the equatorial Atlantic and the East of the 
North Pacific as characterized by a comparatively large 
seismicity. 

Regarding Milne's charts referred to above we shall have 
more to say in chapter xii. It will suffice here to mention 
that the evidence is derived from the seismograms of 
unfelt earthquakes obtained from more than forty stations 
widely distributed over the earth's surface. From a com- 
parison of the records of any one world-shaking earth- 
quake, it is possible to fix within certain limits the position 
of the epicentre. I reproduce the last chart prepared by 
Milne and presented in the annual report to the British 



VI 



EARTHQUAKE DISTRIBUTION 



97 



Association which met in Leicester in August, 1907. The 
origins are found to lie within the various oval regions 




FIG. 26. The dotted ovals are Milne's seismic districts. The full lines 
are drawn in accordance with de Ballore's statistics. 

marked off by dotted lines. The small type numbers 



98 EARTHQUAKE PHENOMENA VI 

represent the individual earthquakes of which instrumental 
records were obtained practically from all the stations 
indicated on the chart. The number is marked in the 
approximate epicentre of the corresponding earthquake, and 
is the tabulated number of the shock according to Milne's 
own catalogue at Shide, Isle of Wight. The different 
districts are named by the letters of the alphabet from 
A to M \ and the large type numbers give the total number 
of earthquakes which had their origins in the corresponding 
region between the years 1899 and 1905, the interval of 
time over which this method of determination has been 
available. 

De Ballore has criticized this method on several grounds, 
the most important being that Milne's charts indicate 
origins to be in regions which ordinary earthquake statistics 
show to be aseismic, and that certain well-known seismic 
areas do not appear on Milne's charts at all. This argu- 
ment, however, loses a good deal of its force when we realize 
that there are destructive earthquakes which do not shake 
the whole earth. They originate near the surface, are of 
the kind known as volcanic shocks, not tectonic, and have 
therefore a very evident effect in epicentral regions ; but 
they are not intrinsically intense enough to send measurable 
disturbances over the whole earth. The destructive charac- 
ter of an earthquake as experienced at the epicentre depends 
directly on its intrinsic intensity and inversely on its depth. 
A deep-seated but powerful disturbance might have less 
destructive effect at the epicentre than a shallow but much 
less powerful disturbance. The former would be recorded 
on delicate seismographs all over the earth's surface, while 
the latter might affect delicate instruments only within 
a comparatively limited area. 

We have, in short, no right to expect absolute agreement 
between the two ways of seismically surveying the globe. 
The one method represented by de Ballore's statistics 
takes into account only episeismic effects strong enough to 
be recognized in peopled districts. The other method deals 
with tremors which have passed through the earth's sub- 
stance, and over the whole circumferential surface. 



VI EARTHQUAKE DISTRIBUTION 99 

To bring out the differences and similarities I have 
entered in full lines on Milne's chart the general results of 
de Ballore's tables of seismicities brought down to the year 
1897 (see Gerland's Beitrdge zur Geophysik, vol. iv). The 
lines of equal seismicities marked I, IV, XVI show the 
localities where the seismicities are respectively 1, 4, and 
16 shocks per annum per 10,000 square kilometres ( =3861 
sq. miles). 

It will be seen that Milne's districts B, C, D, E, F, K 
agree closely with de Ballore's statistics and that A, H 
have a good deal in common. We could not expect the 
antarctic districts L and M to give any direct statistics. 
Thus /, J, and G are the only ones which seem to lie outside 
the seismic areas given by de Ballore's statistics. / and J 
have a very small number of earthquakes associated with 
them and are evidently of little importance ; so that G in 
the Indian Ocean is the only important district which finds 
no place in de Ballore's tables. It is to be noted that this 
district is almost entirely oceanic ; and that many earth- 
quakes originating within it would be very feebly felt in 
neighbouring countries. 

A well-known earthquake region is in European Italy 
and the Alps, having according to de Ballore a seismicity 
equal to that of Japan. This in Milne's chart is a mere 
part of an extensive district, which as a whole is not much 
more seismically active than the region E including Japan. 
Thus Italy and the Alps do not constitute a region specially 
visited by world-shaking earthquakes. Many of the violent 
Italian shocks are indeed of comparatively small extent, 
not being recorded on delicate seismographs at distant 
stations. 

Taking a broad view of earthquake distribution we see 
that the strongly marked seismic regions are situated on 
the borders of continents and in regions where we know 
geological changes to be in progress. Thus all round the 
Pacific Ocean there is a succession of seismic areas, beginning 
with the East Indies and passing north and east by way of 
the Philippines, Japan and Alaska, and then south again 
along the west coast of the two Americas. Another well- 

H2 



100 EARTHQUAKE PHENOMENA VI 

marked region begins in the west of Europe and passes east 
through Sicily, Italy, Greece, Syria, India, and Central 
Asia. The West Indies constitute a district which may 
be taken along with Central America. In these regions are 
contained practically all the known localities subject to 
pronounced seismic activity. The recent catastrophes at 
San Francisco, Valparaiso, Jamaica, and Sumatra are all 
good illustrations. 

As already indicated in chapter i, the prime cause of 
earthquakes is the instability of the earth's crust. This 
instability through geological time is demonstrated by the 
foldings and faults which occur in endless variety ; and 
is connected with the heterogeneity of the crust and with 
the interplay of gravitational and elastic forces. The pro- 
blem to be considered is not, why do earthquakes occur, 
but why do they favour particular portions of the earth's 
surface ? The only answer to this question is that we have 
to do with a fundamental feature of the earth itself. The 
broad distribution of heights and depths, of land and water, 
must be accepted as a condition whose lines were laid down 
in the remote past, and whose development has been the 
natural result of the interplay of gravitational, cohesive, 
and elastic forces in a material crust of definite hetero- 
geneity. Given a particular distribution we may be able 
to follow out the changes which these forces necessarily 
compel; but some initial heterogeneity we must assume. 
There is no getting behind this fundamental fact. 



CHAPTER VII 

PERIODICITIES 

Earthquake Frequency. Possible Causes. Tidal Stresses due to Sun and 
Moon. Annual and Semi-annual Periodicities. Method of Analysis. 
Rayleigh and Schuster's Application of Theory of Probabilities. 
Expectancy in Hap-hazard events. Author's original Investigations. 
Davison's corroborative work. Annual Frequency in Northern and 
Southern Hemisphere. Possible Meteorological Causes. Slow Baro- 
metric changes. Omori's Discussion of Japan Earthquakes. Criti- 
cisms and Conclusions. Rainfall, Snowfall, Denudation, Deposition. 

IN the preceding chapter we have seen that the prime 
cause of earthquakes is the heterogeneity of the earth's 
crust combined with an approximate state of equilibrium 
or isostasy which is constantly breaking down under re- 
adjustments. In regions where shocks are frequent the 
material of the crust is in what might be called a seismically 
sensitive state ; and it is conceivable that under the influence 
of external periodic forces the crust may yield in a similar 
periodic manner. This consideration is the scientific founda- 
tion for the many attempts which have been made to trace 
possible periodicities in earthquake frequencies in various 
districts, small or large. 

In 1885 I communicated a paper on Earthquake Fre- 
quency to the Transactions of the Seismological Society of 
Japan ; a Society which ceased to exist in 1892, and of 
which the Transactions are not readily accessible outside 
seismological observatories and certain scientific societies. 
For these reasons I propose to quote with slight verbal 
changes certain introductory paragraphs. 

' Earthquake Frequency depends on two distinct things 
the seismic sensitiveness of the region, and the existence 
at the proper time of a stress suitably applied. 

'Now if there is any marked periodicity in earthquake 
frequency, there must be a corresponding periodicity in 
either or both of these two independent factors. It is 
possible of course that there may be a natural period in the 



102 EARTHQUAKE PHENOMENA VII 

growth of the sensitiveness of a given region from one time 
of yielding to that degree of sensitiveness necessary for the 
next ; but it is difficult to believe that such a periodicity 
would be generally characteristic of all regions, or of such 
purely terrestrial causes as have been specified. Since our 
object is to discuss periodicity as displayed in earthquake 
frequency over the whole globe, we may confine our attention 
simply to the various cosmic and meteorological phenomena 
which may possibly influence seismic activity. In so con- 
fining our attention, however, we must not be understood to say 
that these are the causes of earthquakes, but merely that they 
are possible determining factors in earthquake frequency. 

' Of all bodies external to the earth the sun and moon alone 
can be expected to produce any appreciable effect in virtue 
of direct gravitational action. The idea that seismic or 
volcanic phenomena are due to tidal actions produced in 
the interior parts of the earth is no new one. In the early 
days of geology, when the earth's solid crust was supposed 
to enclose a molten interior, such an idea was a very natural 
one. With this theory as a guide, geologists tried to find 
some relation between the moon's altitude and the intensity 
of volcanic eruption, but with small success. In 1839, the 
theory of the liquid interior enclosed by a thin solid shell 
received its death-blow at the hands of Hopkins, who 
showed that such a structure was quite incompatible with 
the astronomical phenomena of precession and nutation. 
Not only would the tides produced in the fluid interior 
utterly do away with precession as it exists ; but the thin 
crust would have to be of infinite rigidity to be able itself 
to resist the deforming tidal action. That precession and 
nutation might be as they are, the whole crust, supposed 
rigid, would have to be at least 800 miles thick. In 1862, 
Sir William Thomson [afterwards Lord Kelvin] followed up 
Hopkins's researches by a discussion of the problem of the 
yielding of the earth to tidal action. That it must yield 
to some extent is indisputable, since certainly its rigidity is 
not infinite. But whether the amount of yielding is per- 
ceptible to observation is a very different question. The 
effect of such a yielding, if appreciable, would show itself 



VII PERIODICITIES 103 

in the ordinary ocean tides on the earth, diminishing their 
apparent magnitudes. For the direct solution of this 
question the British Association, on the motion of Kelvin, 
appointed a committee to make careful tide measurements. 
These, together with the valuable tidal observations pub- 
lished by the Indian Government, have been worked up by 
G. H. Darwin, whose elaborate papers on the tidal stresses 
in viscous and elastic globes rank among the classical 
memoirs of the [nineteenth] century. Besides the usual 
solar and lunar diurnal tides known to every one, there are 
tides of long periods not generally mentioned in elementary 
textbooks. These are the fortnightly, the monthly, the 
semi-annual, and annual tides. The first and third arise 
respectively from changes in the moon's and sun's declina- 
tions, or angular distances N. or S. of the equatorial plane ; 
the second and fourth from changes in their linear distances 
from the earth. Thus, when the moon's declination is zero 
there is on the whole higher water at the equator and lower 
water at the poles than when the declination has any other 
value. Hence there is a small fortnightly oscillation in the 
values of the semi-diurnal tides as the moon passes from 
node to node ; and a similar effect with a half year period is 
produced by the sun's motions in declination. In one 
revolution again the moon's distance from the earth goes 
through a complete cycle from apogee to apogee. In perigee 
the tidal effect, which varies inversely as the cube of the 
distance, is of course at a maximum. And thus arises the 
monthly tide ; and similarly the annual tide. Of these the 
fortnightly and monthly tides are much the larger ; and it 
is from them that . Darwin draws his conclusions. One 
advantage in taking these long periodic tides from which to 
calculate is that, if the earth really does yield, it has time to 
make an adjustment which can be treated on the ordinary 
equilibrium theory. In all probability the semi-diurnal tidal 
stresses are too rapid to produce measurable deformation in 
the solid earth. This question of time in producing strain 
in viscous or solid matter is really a most important one, 
and seems to have been quite overlooked in earthquake 
literature. We shall return to it later. Darwin's method, 



104 EARTHQUAKE PHENOMENA VII 

then, consists in expressing by means of suitable formulae 
the fortnightly and monthly tides. In these there enter 
certain unknown co-efficients, which however have different 
definite values or relations to each other, according as the 
earth yields as a whole or is infinitely rigid. By combining 
the tidal observations of India, Britain, and France, he 
deduces the most probable values of these co-efficients ; and 
the final result is that although " there is some evidence of 
a tidal yielding of the earth's mass, that yielding is certainly 
small, and that the effective rigidity is at least as great as 
that of steel ". 

' This conclusion, that the earth as a whole is as rigid as 
an equal sized globe of steel, seems at first somewhat startling 
especially to one who has no very clear notion of what is 
meant by the term rigidity, but regards it as synonymous 
with inflexibility. A window pane will rather break than 
bend ; and yet a glass fibre can be used as a thread. The 
rigidity is the same in both cases, but the inflexibility is 
much higher in the one case than in the other. The same 
truth is illustrated in the behaviour of a steel hair-spring 
and a steel bar. Thus the mere existence of magnificent 
foldings or rumplings in the hard rocky strata that form the 
earth's crust can tell us absolutely nothing regarding the 
rigidity of the material. A sheet of the hardest steel of the 
same form and size as (say) a stratum of old Red Sandstone 
would go through very similar transformations under the 
continued moulding action of the powerful stresses that are 
known to exist within the earth's substance. To measure 
rigidity we must know not only the strain produced but the 
stress which produces it. No purely geological method can 
lead us to a knowledge of what this stress is ; it can be 
estimated from the strain only when the rigidity is known. 
Laboratory experiments, however, are of little use in this 
quest, since we have access to a very limited part of the 
earth's substance ; and even had we access to the deeper 
regions of our globe the samples finally experimented on would 
certainly have quite changed their properties when brought 
from their warm high pressure depths to the light of day. 

'Darwin has proved, then, that if there exists any tidal 



VII PERIODICITIES 105 

yielding of the earth as a whole it is hardly appreciable, 
even when searched for by our most refined methods of 
analysis. Still, although there may be no yielding as 
a whole, there must be time variations in the tidal stresses 
at any given point ; and these may cause earthquakes if 
the region chance to be seismically sensitive. No one so 
far as I know has grouped earthquakes according to lunar 
or solar declination. Perrey made elaborate comparisons 
between earthquake frequency and the position of the moon, 
and obtained apparently definite results. He found that the 
frequency of earthquakes increased at syzygies, at apogee, 
and at meridian passage. The last can hardly be accepted 
as indicating any physical relation, for it is surely impossible 
for such a short-timed periodic change to have any such 
pronounced effect. Then, according to Chaplin, 1 the Japan 
earthquakes have a minimum of frequency at syzygies ; 
and the still more recent discussion by Forel 2 of the Swiss 
earthquakes throws strong doubt on any such relation. He 
finds only 53 per cent, of the total number occurring during 
the syzygy period. The same percentage is brought out for 
the earthquakes occurring at the meridian passages of the 
moon. It might be interesting to tabulate earthquakes 
according to the moon's declination 3 though it is extremely 
doubtful if the result obtained would have a value at all 
worthy of the labour involved. It is possible, however, 
that this fortnightly oscillation of the direction of maximum 
tidal stress in the earth's substance may be a determining 
factor in their frequency. 

' Whatever may be the effect of the moon's motion in 
declination, that of the sun's will of course be much less. 
Its distance is greater ; and its motion in declination smaller. 
But on the other hand, the period is longer, so that the earth 
may yield more in proportion to the corresponding variations 
of stress. One suggestive fact in connexion with these 
motions in declination is that earthquakes abound in 
tropical and sub-tropical regions just where the tidal stresses 

1 Transactions of Asiatic Society of Japan, vol. vi. 

2 See IS Astronomic (January, 1884). 

3 This I did later see below, chapter viii. 



106 EARTHQUAKE PHENOMENA VII 

are greatest, and where also the fortnightly and semi-annual 
variations most tell. Then there is the solar annual tide, 
due to the periodic change in the sun's distance. The effect 
of this would be to cause greater earthquake frequency in 
the half year from September to March, that is in our winter. 
In the northern hemisphere there is a very marked winter 
maximum of frequency ; but in the southern hemisphere 
the maximum seems to come between June and September, 
while in certain equatorial regions there is no definite annual 
periodicity at all. We must not, however, conclude hastily 
that the annual tide has no effect ; all we can say is, that 
there is some other more efficient cause tending to produce 
earth tremors in the winter season, wherever there is a well- 
marked winter season. Still it is well to consider more in 
detail what features might be expected to accompany 
a periodicity determined by the semi-annual and annual 
tides. As already pointed out, the torrid zone, with imme- 
diately contiguous zones to the north and south, would be 
the seat of most frequent seismic actions. Then, the semi- 
annual maximum would occur at localities in higher latitudes 
during the local summer ; while the annual maximum would 
occur about December or January, to allow for the lagging 
of strain after stress. At equatorial places, the semi-annual 
effect would really have a quarter-yearly period ; while at 
points lying in the 10th or 12th latitude line, both north 
and south, this effect would vanish. In many of the 
statistics there are indications of semi-annual periods as 
for example in Mallet's general curve of frequency for the 
whole northern hemisphere. 1 In searching for such semi- 
annual periods, we must adopt some means for smoothing 
off the jaggedness in our curve of frequency and eliminating 
the annual period. The method which seems to me to be 
least open to objection is to take overlapping means of the 
numbers originally obtained. 

' Hitherto it must be confessed there has been a good deal 

of arbitrariness in the treatment of earthquake statistics. 

As a rule, earthquakes are numbered in monthly groups, 

which are then combined in seasonal sets. Mallet called 

1 British Association Reports (1858). 



VII PERIODICITIES 107 

January, February, March, the winter months a nomen- 
clature to which strong objection may well be taken and 
his example has been generally followed. December, 
January, February, are certainly a truer seasonal combina- 
tion, thus making Spring begin on the 1st of March, Summer 
on the 1st of June, and so on. But this grouping in months 
is purely arbitrary since our month is a civil and not 
a natural division of time. Such a grouping may indicate 
the existence of long periods, but it affords no ready means 
of distinguishing between the co-existence of several distinct 
long periods. To do so, we must devise some method of 
analysing the complex period shown in these monthly sums. 
For the northern hemisphere there is a well-marked annual 
period in earthquake frequency. Is there a Semi-annual 
period ? such as might be caused by the changes in the 
sun's declination. 

' To answer this question we must do three distinct opera- 
tions. We must prepare our numbers by some strictly 
accurate mathematical process so as to magnify (first) the 
annual effect and (second) the semi-annual effect, smoothing 
away somewhat the effects of the smaller periods. And 
then, by direct comparison of these prepared curves, we 
must separate out the semi-annual period. 

* Take for example Professor Milne's catalogue of Japan 
earthquakes from 1872 to 1880 inclusive, arranged according 
to months. Form three-monthly means, tabulating under 
January the mean of December, January, February ; under 
February the mean of January, February, March ; under 
March the mean of February, March, April ; and so on 
through the whole twelve months. The effect of this 
operation is to magnify the annual and semi-annual periods 
at the expense of the shorter periods ; while the quarter 
annual period, eighth-annual period, sixteenth-annual period, 
if there are any, vanish. Beginning again with the original 
monthly numbers, take the six-monthly overlapping means, 
and tabulate them as follows : set the mean for the months 
from January to June halfway between March and April; the 
mean from February to July halfway between April and May; 
and so on. By this process we throw out completely semi- 



108 EARTHQUAKE PHENOMENA VII 

annual, quarter-annual, eighth-annual, &c., periods, and 
diminish very markedly the effect of all other possible periods. 

'Now it can be shown by an application of Fourier's 
Theorem that from these two curves a third curve may be 
obtained from which the annual period is completely 
eliminated. To effect this, the three-monthly means must 
be reduced by multiplying by the factor -707. In this way 
we obtain a prepared semi-annual curve with the annual 
periodicity involved exactly a s it is involved in the annual 
curve formed from the six-monthly means.' 

Applying this method of investigation to selected material 
available at the time I discussed the annual and semi-annual 
periodicities of earthquakes in Japan, Europe (Perrey's list 
as given by Mallet), New Zealand, East Indian Archipelago, 
Chili, and Grecian Archipelago. By an oversight I inverted 
the semi-annual curve, so that what was formerly described 
as the maximum should be the minimum, and the minimum 
the maximum. 

Since 1884, statistics of earthquakes have accumulated 
at an increasing rate from all parts of the world ; and in 
a paper on the Annual and Semi-annual Seismic Periods, 1 
Dr. Davison followed up these early investigations by 
making use of a much larger body of statistics. He used 
a slightly modified method of reduction, and deduced not 
only the times of the maxima and minima, but also com- 
pared the amplitudes of the annual and semi-annual periodici- 
ties. With the correction of the oversight mentioned above 
his results corroborate those obtained in 1884. 

It is convenient at this stage to consider the general 
question of the search of periodicities in given statistics. 
The recognized mathematical method is that furnished by 
Fourier's analysis of a complex harmonic function into its 
simple harmonic components. Given, for example, a body 
of statistics of earthquakes arranged as above according 
to the month of occurrence, we obtain a set of numbers, 
twelve (or, better, twenty-four) in all, giving the frequencies 
in the successive months (or half months) from January to 
December. If we measure along a horizontal line twelve 
1 Philosophical Transactions, vol. clxxxiv, 1893. 



VII PERIODICITIES 109 

equal intervals, representing the successive months, and 
draw at the middle point of each a vertical line representing 
to an assumed convenient scale the corresponding frequency, 
we obtain a graph showing to the eye the march of fre- 
quency with time throughout the year. This represents 
a complex harmonic function of the time. By means of 
Fourier's theorem we can analyse this function into simple 
^armonic components, the periods of which are as the 
reciprocals of the natural -numbers, 1, 2, 3, 4, &c. The 
period of the first component is one year, of the second 
half a year, of the third four months, of the fourth three 
months, and so on. 

In regard to the value of Harmonic Analysis in such 
investigations my opinion has considerably altered in 
recent years. It is a purely mathematical method and leads 
to results which have in many cases no physical meaning. 
For example, in the present inquiry our hope is to obtain 
well-marked annual and semi-annual periods ; but the 
Fourier analysis may give in addition a period of a third 
of a year with a well-marked amplitude. We might expect 
that this third harmonic might become less and less signifi- 
cant as we based our investigation on a greater and greater 
number of events. But this expectation is founded on the 
hypothesis, generally made unconsciously, that the acting 
causes which give rise to the first and second harmonics 
are themselves of a simple harmonic form. Every attempt 
to analyse a complex harmonic function into simple har- 
monic components is either a purely mathematical operation 
enabling us simply to build up the original function by 
putting together the components again, or, if it has any 
physical significance at all, it is based implicitly on two 
very doubtful assumptions, (1) that the acting causes are 
themselves simple harmonic in their variation, and (2) that 
this simple harmonic quality is dynamically reproducible in 
the system acted upon. The whole theory of forced vibra- 
tions already discussed in chapter v shows how unwarranted 
this latter assumption may be. 

But even were the method of harmonic analysis theo- 
retically unobjectionable, it is extremely doubtful if the 



110 



EARTHQUAKE PHENOMENA 



VII 



character of earthquake statistics is such as to warrant us 
in undertaking the labour involved in applying the Fourier 
analysis. Twelve years ago I went through this labour in 
connexion with the lunar periodicities discussed below ; 
but I am now convinced that sufficient accuracy is attained 
by use of the purely arithmetical overlapping summations 
over suitable intervals. This is essentially the same method 
as that of the overlapping means used by myself in 1884*. 
and by Davison in 1893. 

To illustrate the method which is adopted consistently 
throughout the present discussion, take the case already 
referred to, namely, Milne's catalogue of Japan earthquakes 
from 1872 to 1880 inclusive. This I take because it is 
historically the first set of statistics to which the arith- 
metical method for separating out the annual and semi- 
annual periods was applied. 

The monthly frequencies are first arranged in a column, 
and from these a second column is formed of six-monthly sum- 
mations, each summation being set exactly half-way down 
the six-monthly numbers from which it has been formed. 





Monthly 
whole year 


Six-monthly 
summations 


Monthly 
half-year 


Three -monthly 
summations 


Jan. 


29 




58 


189 






207 






Feb. 


36 




57 


166 






202 






Mar. 


38 




51 


166 






194 






Apr. 


26 




58 


178 






194 






May | 32 




69 


201 






179 






June 


33 




74 


201 






154 






July 


29 












160 






Aug. 


21 












165 






Sept. 


13 












173 






Oct. 


32 












173 






Nov. 


37 












188 






Dec. 


41 












213 







VII PERIODICITIES 111 

The third column, headed ' monthly half-year ', is formed 
by adding the frequencies of each pair of numbers six months 
apart, that is, January and July, February and August, and so 
on. From these the fourth column of numbers is formed by 
taking overlapping three-monthly summations. The second 
and fourth columns give respectively, to a sufficient approxi- 
mation, the annual and semi-annual periodicities. The annual 
periodicity shows a marked maximum between December 
and January, with a minimum between June and July. The 
difference between the maximum and minimum divided by 
the total number of earthquakes, namely (213 154)/367 
or 0-161, gives what may be called the uncorrected relative 
amplitude. Similarly for the semi-annual periodicity we 
find 35/367 = 0-095 ; and the maximum falls between May 
and June and also between November and December. 

This method of preparing the numbers in order to be able 
to apply to the semi-annual periodicity the method already 
used for deducing the annual periodicity is the modification 
introduced by Davison. It is simpler of application and 
not less accurate than the method originally used by me. 

We must now consider how to correct the relative ampli- 
tude so as to obtain what may be regarded as the true value 
of the amplitude in the periodic variation under discussion. 
Let us suppose that the function is of the form 

f =F+A cos(t+a)+Bcos(2t+b)+&c. 
where t is the time expressed in the unit of which 2ir or 
6-2832 represents the complete period under discussion. What 
we use in the statistical discussion is not/ but the summation 
or integral of / through a limited fraction of the period, in 
the present case, half a month. Let 2ir/n represent this 
limited interval of time. Then the tabulated frequencies 
may be represented by the expression 

2r7T F + 2A sin 77 cos (t +a) 
n n 2w 

n cos (2t+b) 



2ir _, ( A sin IT /n 
= F\l + -jj- / cos Z+a 
n I F -n/n 



B sin 27iAi 

cos 
F 2ir/n 



,. } 

(2t +b) + .> 

3 



112 EARTHQUAKE PHENOMENA VII 

This quantity we then treat by overlapping summations, 
Avhich correspond to integrations over half the period. We find 

-4 sin v/n 2 sin ir/2 
~ 



F 



COS 



B sin 2 



sin Trn 2 

+ a) 



r / 

w- ( F 7r/n TT. 

the term in 5 vanishing because sin IT = 0. 

Thus the unconnected relative amplitude is equal to the 
true relative amplitude A/F multiplied by the factor 

2n . TT 
- sin - 

TI" n 

where 1 /n is the fraction of the whole period in terms of which 
the frequencies are tabulated. In the case already dis- 
cussed, n is 12 for the annual, 6 for the semi-annual. When 
the frequencies are tabulated by half-months, then the 
corresponding numbers will be 24 and 12, with 6 for the 
quarter-annual. When we come to discuss the lunar 
monthly periods, the frequencies are tabulated by days, 
and n is 28 or 30 according to the kind of month, and 14 or 
15 for the half -monthly period corresponding. Again, in 
the solar daily and half -daily periods, n is 24 and 12 respec- 
tively ; while in the lunar daily and half-daily statistics we 
take n equal to 25 and 12-5 respectively. It is convenient 
to calculate the factor for these various cases, as in the 
following table : 

n = 3 6 12 24 12.5 25 oo 

?| sin -=-527 -608 -629 -634 -630 -635 -637 
TT n 

Hence to pass from the uncorrected amplitude to the true 
relative amplitude we divide by one or other of these frac- 
tions, according to the method of grouping adopted. 

For values of n above 6 the factor does not change much 
in value ; and in most cases when all that is aimed at is 
a comparison of the amplitudes of the harmonic components 
whose periods are as 1 to 1/2, the uncorrected amplitudes 



VII PERIODICITIES 113 

are sufficiently accurate. There is, however, another con- 
sideration which compels us to introduce these factors. 

In 1897, Professor Schuster communicated a paper to the 
Royal Society of London on Lunar and Solar Periodicities 
of Earthquakes, which was to a large extent a critical 
examination of the results indicated in my somewhat earlier 
paper on the same subject. These will be discussed later. 
It is important, however, to refer at this place to Schuster's 
critique, which furnishes a criterion as to the reality of an 
apparent periodicity in such statistics as we are dealing with. 

The question is one of probabilities ; and, developing 
a result given by Rayleigh in 1880, Schuster draws certain 
conclusions which may be described in the following terms. 
Suppose that we have n disconnected events occurring at 
random within a given interval of time, and that we consider 
the probability of the frequency of these events being 
expressed harmonically by a Fourier series in which the 
periods are submultiples of the interval of time ; then it is 
shown that the probability of any amplitude lying between 
the limits r and r+dr is 

\nr dr e~ nr2 /* ; 

that the expectancy for the value of the amplitude is 
V(it/ri) ; and that the probability of the amplitude exceed- 
ing any given value p is exp ( np 2 /!). 

To appreciate the bearing of this application of the 
mathematical laws of probability, consider the annual 
periodicities of three cases worked out in my first paper 
of 1886, namely, Perrey's list of European historic earth- 
quakes as given by Mallet, the list of Japanese shocks 
reproduced above, and the shocks experienced in the Grecian 
archipelago. The number of independent shocks in these 
cases were, respectively, 1961, 367, and 3587. The corre- 
sponding values of Schuster's ' expectancy ' are 0-04, 0-0925, 
0-0296. The uncorrected relative amplitudes are 0-14, 0-14, 
and 0-102, giving, when divided by 0-63, the corrected 
values 0-22, 0-22, and 0-16. In the first and third cases the 
amplitudes are distinctly greater than the calculated expec- 
tancies ; but although the amplitude is greater than the 



114 



EARTHQUAKE PHENOMENA 



VII 



expectancy in the case of the Japan statistics, it is not 
markedly so. The probability that the amplitude should ex- 
ceed 0- 2, the events being assumed to be disconnected, comes 
out in the respective cases, l/(33 x 10 7 ), 1/39, I/ (38 x 10 H ). 
Thus, even in the case in which the relative amplitude is 
a little more than twice the expectancy for random discon- 
nected events, the probability that these will give a value 
greater than the amplitude obtained is only 1 in 40. 

The following table gives the probabilities that the ampli- 
tudes should exceed successive multiples of the expectancy 
E, and shows how rapidly the probability diminishes as the 
multiples increase. 

Amplitude = E 2E 3E 4E 5E QE SE IOE 
Probability = 0-456 -0432 -0 3 85 -0 5 35 -0 8 3 -0 12 52 -0 21 15 -0 34 78 

The suffix after each zero indicates how many zeros there 
are after the decimal point. When the amplitude reaches 
four times the expectancy the probability is so small that 
we are justified in regarding the existence of such an ampli- 
tude as evidence of a real periodicity. 

We now proceed to consider the evidence furnished by 
various sets of statistics of earthquake frequency. 

I give first a table containing the results deduced from 
the six sets of earthquake statistics which I discussed in 
1884. The successive columns of the table give the name 
of the region, the interval of time over which the statistics 
extend, the number of shocks catalogued, the month in 
which the annual maximum occurs, the (earlier) month in 
which the semi-annual maximum occurs, the corrected 
relative amplitudes, and the ' expectancy ' according to 
Schuster's theory. 



Region 


Time 
Interval 


No. of 
Shocks 


Month of Maximum 


Amplitude 


Annu.il 


Semi-arm. 


Annual 


Semi-ann. 


Japan . . 


1872-80 


367 


XII-I 


Ill 


0-256 


0-157 


Europe 


306-1843 


1961 


XII 


I 


0-22 


0-12 


N. Zealand 


1869-79 


585 


VIII-IX 


II 


0-203 


0-161 


E. Indian 


1873-81 


515 


VIII, X, 


III 


0-071 ? 


0-099 


Archip. 






or XII? 








Chili . . 


1873-81 


212 


VII 


VI 


0-48 


0-17 


Grecian 


1859-81 


3578 


XII-I 


III 


0-164 


0-268 


Archip. 















Expectancy 

%/(/) 

0-093 
0-04 
0-073 
0-078 

0-122 
0-03 



VII PERIODICITIES 115 

These all, with one important exception, indicate a marked 
annual periodicity, with amplitudes well above the expec- 
tancy value for disconnected events. The time of maximum 
is, in every case, during the winter season. The one 
exception is the case of the East Indian Archipelago, for 
which the earthquakes show no distinct tendency to 
a maximum, and for which there is no marked winter 
season. 

Before discussing the significance of these results let us 
consider the corresponding results obtained by Davison 
from the much larger body of statistics to which he had 
access ten years later. 

It seems to me that in many cases the statistics utilized 
l)y Davison are too meagre for the purpose proposed ; and 
it is doubtful if, even in the best sets of statistics, we should 
lay any great stress on numerical details. Some of the 
catalogues at our disposal cover centuries, and yet the 
number of earthquakes recorded does not exceed a few 
thousands. These are, of course, large shocks which receive 
mention in ordinary historic records. Very recent cata- 
logues, again, are in default in another direction. They 
extend over too small an interval of time. In other cases 
the interval of time may be sufficient, but the total number 
of shocks is so small as to give an average of less than 
20 a year. It is evident that in such cases, unless the 
interval is distinctly long, extending over a century or two, 
the statistics are really not sufficient to serve as a basis for 
calculations in periodicities. 

Of the 62 different sets of records made use of by Davison, 
only 23 may be regarded as satisfactory, and about 7 others 
barely admissible. It is impossible, for the reasons given, 
to place any confidence in results deduced from the remain- 
ing 32 cases. 

In the following table, constructed on the same principle 
as that just given, I have arranged the sets of records which 
seem worthy of consideration, leaving out those sets already 
discussed by me and rediscussed by Davison. 

Because of the comparatively small annual frequency tho 
last five are of little account. 

i 2 



116 



EARTHQUAKE PHENOMENA 



VII 



EABTHQTJAKE STATISTICS (DAVISON) 



ttpcrinn 


Limiting 


No. of 


Maximum Month 


Amplitude 


Expect. 


itegiuii 


Dates 


Shocks 


Annual 


Semi-ann. 


Annual 


Semi-ann. 


A/Or/n) 


N. Hemisphere . 


223-1850 


5879 


XII 


II 


0-11 


0-07 


0-023 


N. Hemisphere . 


1865-84 


8133 


XII 


IV 


0-29 


0-11 


0-02 


Europe .... 


1865-84 


5499 


XII 


IV 


0-35 


0-11 


0-024 


Austria .... 


1865-84 461 


I 


V-VI 


0-37 


0-22 


0-083 


Switzerland and 
















Tyrol .... 


1865-83 


524 


I 


VI 


0-56 


0-37 


0-077 


Italy .... 


1865-83 


2350 


IX, XII 


IV 


0-14 


0-14 


0-037 


Italy, excluding 
















Sicily and Vesu- 
















vius .... 


1865-83 


1513 


IX, XI 


IV 


0-21 


0-17 


0-046 


Vesuvius District 


1865-83 


513 


XII 


VI 


0-25 


0-25 


0-078 


Italy 
Old Tromometre 


1872-87 


61732 


XII 


V-VI 


0-49 


0-08 


0-0071 


Old 


1876-87 


38546 


XII 


V 


0-46 


0-04 


0-0093 


Normal 


1876-87 


38546 


XII 


V 


0-49 


0-03 


0-0093 


S. E. Europe . . 


1859-87 


3470 


XII 


III 


0-21 


0-25 


0-03 


Balkan, &c. . , 


1865-84 


624 


XII 


II 


0-27 


0-37 


0-071 


Zante .... 


1825-63 


1326 


VIII 


VI 


0-10 


0-19 


0-049 


Japan .... 


1885-89 


2997 


X 


III 


0-08 


0-07 


0-032 


Japan .... 


1876-81 ) 
1883-91 \ 


1104 


II 


V 


0-19 


0-21 


0-053 


Japan .... 


1878-81 


246 


XII 


I 


0-46 


0-19 


0-113 


Malay Archip. . 


1865-84 


598 


V 


I 


0-19 


0-25 


0-072 


S. Hemisphere . 


1865-84 


751 


VII 


I, III 


0-37 


0-06 


0-065 


New Zealand . . 


1868-90 


641 


III, V 


II 


0-05 


0-13 


0-070 


Chili 


1865-83 ? 


316 


VII, XII 


IV 


0-27 


0-11 


0-100 


Hungary, &c. . . 


1865-84 


384 


XII 


VI 


0-31 


0-30 


0-090 


Asia 


1865-84 


458 


II 


II 


0-33 


0-14 


0-083 


N. America 


1865-84 


552 


XI 


IV 


0-35 


0-14 


0-075 


California . . . 


1850-86 


949 


X 


IV 


0-30 


0-16 


0-058 


Peru, Bolivia . . 


1865-84 


350 


VII 


I 


0-48 


0-24 


0-095 



An examination of the larger table will be found to 
corroborate in a remarkable way the conclusions derived 
from the much smaller body of statistics used in 1884. 
These early statistics were to some extent selected with 
a view of testing the existence of a ' seasonal ' periodicity 
which might be connected with meteorological rather than 
with gravitational tidal effects. 

Thus we see that, with three exceptions, namely, Zante, 
the Malay Archipelago, and (what is practically the same) 
the East Indian Archipelago, the maximum annual frequency 
occurs in a winter season month. This month is December 
in the great majority of the northern hemisphere regions ; 



VII 



PERIODICITIES 



117 



while in the southern hemisphere the maximum frequency 
falls in the autumn and winter seasons of that hemisphere. 

The Malay Archipelago statistics given by Fuchs, on 
which Davison based his discussion, show a somewhat small 
maximum in May, whereas the East Indian statistics which 
I used gave no clear annual maximum. In this latter case 
the semi-annual maximum is not much greater than the 
expectancy, whereas Fuchs's statistics give a semi-annual 
amplitude fully three times the expectancy. Fuchs's 
statistics cannot be very complete, for he gives 598 shocks 
in nineteen years, while Bergsma, who was my authority, 
gave 515 shocks in only eight years. 

To bring out the broad distinction of the annual variation 
of earthquake frequency in the two hemispheres I reproduce 
the statistics as given by Fuchs and arranged by Davison. 
They are grouped in half-month intervals, each number in 
the lower line referring to the second half of the month named. 



Hemisphere 


J. 


P. 


M. 


A. 


M. 


J. | J. 


A. 


S. 


0. 


N. 


D. 


Northern . 
1865-84 . 
Southern . 
1865-84 . 


|342 
409 
35 
25 


344 
338 
24 
23 


403 
405 
23 
35 


286 
269 
23 
23 


345 

285 
22 
20 


242 i 269 
256 I 321 
40 ' 33 
45 | 43 


237 
244 
41 
47 


252 

318 

27 
23 


343 
422 

48 
53 


487 
505 
31 
33 


437 
374 
$18 
16 



The numbers show at a glance that the frequency in the 
northern hemisphere is fully ten times that in the southern 
a fact which is immediately attributable to the greater 
diversity of land and sea in the northern hemisphere. 

In the diagram I reproduce Davison's graphs of the annual 
and semi-annual periodicities for the two hemispheres. The 
full line curves refer to the annual periodicity ; the dotted 
lines to the semi-annual. 

The seasonal significance of the annual periodicity is 
undoubted ; in each case the maximum frequency falls in 
the winter season. The greater range in the case of the 
southern hemisphere is to be attributed to the smaller 
number of earthquakes involved. But it is otherwise with 
the semi-annual graph. There, in spite of the much smaller 
number of items in the statistics, the semi-annual perio- 
dicity is distinctly less marked in the southern hemisphere 



118 EARTHQUAKE PHENOMENA VII 

than in the northern. When, however, we consider the 

M 



X 




FIG. 27. 
' Expectancy ' (see the table on p. 116) we cannot regard the 



VII PERIODICITIES 119 

apparent semi-annual periodicity as established. In 1884 
I wrote that c the present investigation certainly indicates 
a semi-annual period, but an accumulation of observations 
is needed to establish it as more than conjectural '. Writing 
now, twenty- two years later, I confess that the evidence is, as 
a whole, no stronger than it was. There is too great a variety 
in the times of the maxima, and the amplitude in many cases 
is also too small when due regard is paid to the number of 
observations which form the basis of the investigation. 

At the same time a comparison of the graphs for the two 
hemispheres suggests the possibility of a semi-annual 
periodicity which must be due to a cause less effective in 
the southern than in the northern hemisphere. 

In 1884 I was led by a process of exhaustion to the con- 
clusion that the only two possible causes of the annual 
and semi-annual periodicities were accumulations of snow 
over continent-areas and slow variations of barometric 
pressure, to which might be added rainfall, denudation, and 
deposition. The summary of the argument was as follows : 

' The cause of earthquakes is probably to be referred to 
the earth's heterogeneity of structure or to the inequality 
of stress due to irregularities of its surface. Rupturing or 
yielding is not determined by the amount of stress only ; it 
depends in great measure upon how the stress is applied. 
For rupture to take place the stress must be different in 
different directions ; and the difference between the greatest 
and least stresses is an important datum in estimating the 
tendency to break. So far as can be judged, the only 
periodic stresses that exist of period long enough to tell 
upon the earth's substance are the fortnightly, monthly, 
semi-annual, and annual tides, the annual variation of 
snowfall, and the steady annual and perhaps semi-annual 
oscillation of barometric pressure over the earth's surface. 
Inasmuch as the earthquake frequency reaches its maximum 
in winter wherever there is a marked winter season, we 
must pass from the annual tidal stress due to the sun as of 
little account. We seem, however, to find in the accumula- 
tions of winter snow, and in the long period oscillations 
of the atmospheric pressure, two possible determining factors 
in earthquake frequency.' 

The views advanced by Dr. Davison differ from this only 



120 EARTHQUAKE PHENOMENA VII 

in one respect. He has more regard to the annual change 
of pressure over the seismic district itself ; whereas I take 
into account rather the whole manner in which the pressure 
varies across the seismic region. 

On referring to any meteorological atlas and comparing 
the distribution of barometric pressure for the two months 
January and July, we see that in January the areas of high 
pressure are over the continents in the northern hemisphere, 
and over the seas in the southern hemisphere. In July, the 
opposite conditions hold, the low pressure being over the 
continents in the northern hemisphere and over the seas in 
the southern hemisphere. That is to say, in the winter 
season pressure increases over the land surfaces in all but 
tropical regions ; while in the summer season the pressure 
is greater over the ocean. This see-saw of condition is 
particularly well-marked in the northern hemisphere, which 
is characterized by preponderance of continental areas. 
But not only does the pressure increase over the land 
areas in the seasonal winter, but, as is obvious at a glance 
at the isobaric charts, the isobars are more crowded together 
when the land supports the higher pressure than when (in 
the summer season) the high pressure is over the seas. That 
is to say, the gradient is steeper in winter as we pass out 
from the land towards the sea than in summer as we pass 
from the sea to the land. It is with this condition that 
I associate the winter maximum of earthquakes, rather 
than with the purely local state of the barometer. It is 
a condition which tends to increase the slight instability of 
the isostatic state which is always more or less present on 
the margins of continents. It has been pointed out both 
by Davison and Omori that the yielding of the ocean waters 
to changes of barometric pressure prevents any correspond- 
ing changes of pressure on the ocean bottom ; but that fact 
no more affects the distribution over the land and its conse- 
quences than does the much more important daily tide as 
it sweeps over the seas. This barometric gradient is one of 
the factors which affects the isostatic stability, tending, like 
rainfall, snowfall, denudation of material from the heights, 
and its accumulation along shores, to produce an increased 



VII PERIODICITIES 121 

instability which is followed by yielding and by the assump- 
tion of a new and temporarily more stable configuration. 

If we adopt the generally accepted view that earth- 
quakes are slips along faults, we see at once that a 
vertical load, varying in amount as we pass along the 
surface, is just the kind of thing to increase any ten- 
dency to slip which may be present. The mere increase 
of load over a definite area does not seem to me to involve 
of necessity any greater tendency to slip in the region 
immediately beneath. As a matter of fact all barometric 
changes over certain regions are accompanied by gradients 
more or less steep in varying directions ; but during the 
winter months, over the northern hemisphere especially, 
there is a prolonged condition of average barometric distri- 
bution giving a pronounced gradient over the littoral 
countries. This seems to me to be the most plausible 
way of looking at any relation between annual barometric 
change and seismic frequency. 

I have reproduced the argument in some detail because, 
apparently, it was not quite understood as presented in 
my early paper. That paper also contained a hint at 
a possible cause for the semi-annual periodicity of which 
there seemed to be some evidence. This was found in the 
fact that the barometric gradient, that is, the variation of 
pressure along the surface of the earth, really attains a 
second but much smaller maximum oppositely directed 
during summer. For at that season there is minimum 
pressure over the land and maximum over the seas. The 
evidence for the semi-annual periodicity seems to me to be 
somewhat precarious. There is considerable diversity among 
the times of the maxima in the different sets of records. If 
all were like the two of which I have given the graphs the 
evidence would be greatly strengthened. It is at least 
curious that the southern hemisphere shocks should show 
a semi-annual periodicity so much smaller in amplitude 
than that given by the more numerous statistics of the 
northern hemisphere. Also very suggestive is the fact that 
the southern semi-annual maximum occurs at the same time 
as the northern semi-annual minimum, and vice versa. 



122 EARTHQUAKE PHENOMENA VII 

This points to a seasonal effect, just as in the case of the 
annual periodicities ; and the comparative smallness of the 
amplitude of the southern semi-annual periodicity may be 
connected with the fact that in the southern hemisphere 
there is less land and a closer approximation to the uniform 
conditions of all ocean. 

The problem of the annual periodicity in Japan has been 
recently studied with considerable elaboration by Omori. 1 
One of his general conclusions is that Japan may be divided 
into two districts, in one of which the annual maximum 
occurs in winter and in the other in summer. Roughly stated 
the conclusion is that the NE. end of the main island of 
Japan and the E. of Yezo are characterized by a summer 
maximum ; while the west and middle parts (with the 
exception of a few isolated portions of limited extent) are 
characterized by a winter maximum. A critical examina- 
tion of the districts classified by Omori shows that the 
majority of these are insufficient by themselves to establish 
any law of frequency. When dealing statistically with 
a limited district we must have records extending over 
a long period of years to make up for the usually meagre 
number of shocks recorded per year. There is, however, 
a more fundamental source of uncertainty in the separate 
lists prepared by Omori. In investigations of this kind 
we should have regard rather to the source of the shock 
than to the locality where it is felt. For small local shocks 
there is of course no difficulty ; but for shocks felt over 
a fairly wide area it is otherwise. Thus, in the Tokyo list 
which I reproduce here, the Mino-Owari disaster of October, 
1891, is represented by the number 45, whereas in the 
immediately preceding month there are only 4 shocks re- 
corded. In taking his monthly means Omori excluded this 
number 45 on the ground that these were aftershocks of 
a strong earthquake. It is very doubtful if all the 45 were 
so ; but admitting that they were, what is to be said of 
the 1 2 and 1 5 in the immediately succeeding months ? Some 
of these must have been as truly aftershocks of the great 
earthquake of October as the majority of those which were 
1 Publications of the Earthquake Investigation Commission, No. 8, 1902. 



VII 



PERIODICITIES 



123 



felt in Tokyo in October. The same uncertainty applies 
not only to those particular cases (March, 1894, June, 1896, 
and August, 1897) which have been excluded in the taking 
of the monthly means, but also to other cases which have 
not been excluded, namely, January, 1896, with its 42 shocks, 
July and August, 1896, with their 22 and 18 shocks respec- 
tively, some of which must have belonged to the same after- 
shock system as most of the excluded 51 of the preceding 
month, and so on. It is sufficient to mention these cases 
to show how difficult it is to segregate shocks according 
to limited districts. It seems to me that there is a good 
deal of arbitrariness in the manner in which Omori has 
excluded certain numbers and included others. 

Taking the numbers as they stand, however, let us treat 
them so as to deduce the annual and semi-annual periods. 

MONTHLY FREQUENCIES AT TOKYO ( OMORI). 1876-99 



Year 


Month 


Mean 




I 


II 


III 


IV 


V 


VI 


VII 


VIII 


IX 


X 


XI 


XII 




1876 


3 


4 


6 


11 


5 


3 


3 


5 


3 


3 


4 


6 


56 


1877 


4 


5 


6 


5 


8 


9 


6 


4 


1 


8 


6 


9 


71 


1878 


3 


8 


7 


2 


5 


4 


4 


1 


2 


4 


6 


4 


50 


1879 


6 


7 


14 





9 


4 


3 


4 


1 


7 


6 


9 


70 


1880 


9 


9 


6 


6 


2 


9 


8 


4 


1 


3 


10 


10 


77 


1881 


13 


8 


8 


8 


4 


3 


3 


3 


2 


3 


3 


8 


66 


1882 


4 


7 


15 


6 


3 


2 


2 


1 


1 


4 


1 





46 


1883 


6 





3 


3 


6 


2 


3 


1 





1 


3 


4 


32 


1884 5 


2 


8 


2 


9 


4 


1 


4 


2 


8 


8 


15 


68 


1885 


7 


9 


8 


4 


3 


6 





3 


8 


10 


3 


7 


68 


1886 3 


3 


3 


2 


8 


4 


2 


8 


7 


4 


2 


8 


54 


1887 


10 


4 


3 


8 


13 


5 


6 


2 


10 





5 


14 


80 


1888 


4 


15 


7 


7 


11 


9 


9 


7 


11 


4 


13 


4 


101 


1889 


5 


16 


11 


18 


13 


7 


5 


8 


7 


8 


9 


6 


113 


1890 5 


5 


6 


15 


14 


5 


12 


7 


4 


8 


10 


2 


93 


1891 1 


4 


6 


7 


10 


7 


8 


4 


4 


*45 


12 


15 


123 


1892 9 


11 


3 


7 


7 


9 


14 


2 


7 


11 


4 


8 


92 


1893 5 


4 


5 


7 


10 


10 


4 


3 


6 


3 


3 


1 


61 


1894 


7 


8 


*?,3 


11 


9 


9 


6 


3 


8 


4 


8 


5 


101 


1895 


9,0 


9 


8 


17 


11 


12 


11 


5 


10 


17 


6 


3 


129 


1896 


42 


17 


15 


21 


10 


*51 


22 


18 


7 


5 


7 


10 


225 


1897 


11 


18 


11 


8 


17 


6 


11 


*32 


5 


8 


15 


22 


164 


1898 4 


8 


16 


17 


16 


13 


16 


13 


15 


5 


11 


10 


144 


1899 


7 


11 


17 


13 


6 


9 


8 


16 


8 


8 


13 


8 


124 


sum 


193 


192 


215 


205 


209 


202 


167 


158 


130 


181 


168 


188 


2208 


1876-95 
1896-99 


129 
64 


138 
54 


156 
59 


146 
59 


160 
49 


123 
79 


110 

57 


79 
79 


95 
35 


155 

26 


122 
46 


138 
50 


1551 
657 



124 EARTHQUAKE PHENOMENA VII 

The numbers marked with an asterisk are those which 
Omori has excluded in taking the monthly means. Instead 
of utilizing his mode of treatment, which is somewhat crude, 
though possibly no cruder than the material on which he 
builds, I propose to treat the numbers by the method already 
explained. 

A glance at Omori's table shows that during the last four 
years the frequency greatly increased. It seemed important 
in connexion with the criticisms stated above to inquire as 
to how far a short interval of fairly high seismicity agreed 
with a longer interval of distinctly less seismicity. The 
interval from 1876 to 1895, and the interval from 1896 to 
1899, have therefore been treated separately. I have also 
treated the sums of the whole, omitting the monthly 
numbers marked with an asterisk. This should of course 
agree with Omori's conclusions based on the monthly 
means. 

A little consideration will show that whereas the semi- 
annual sums refer to the middle of each month, the annual 
sums refer to the point of separation of two contiguous 
months. This necessarily throws the maximum and minimum 
points of the annual periodicity half a month later than 
the times of occurrence of the maximum and minimum points 
of the semi-annual periodicity ; but this is of no practical 
account since it is grotesque to imagine that statistics of 
the kind can give results correct to half a month. The 
numbers obtained by this treatment are shown in the two 
following tables, in each of which there are four columns 
corresponding to the total sums of Omori's columns for the 
whole period, the same sums diminished by the numbers 
marked with an asterisk, the sums for the interval 1876 to 
1885, and the sums for the interval 1895 to 1899. These 
I shall distinguish by the symbols S, 8', S (20) 8 (4), for the 
six-monthly summations giving the annual period, and 
T, T' 9 T (20), T (4), for the three-monthly summations 
corresponding to the semi-annual periods. 

At the foot of each table are given! the corrected relative 
amplitude, and Schuster's ' Expectancy' 



VII PERIODICITIES 

ANNUAL PERIODICITY (SIX-MONTHLY SUMMATIONS) 



125 



Month 


s 


S' 


5(20) 


0(4) 


I-II 


1161 


1138 


829 


332 


II-III 


1202 


1179 


867 


335 


III-IV 


1216 


1142 


852 364 


IV-V 


1190 


1116 


835 


357 


V-VI 


1156 


1050 


775 


382 


VI-VII 


1071 


988 


714 


358 


VII-VIII 


1047 


919 


723 


325 


VIII-IX 


1006 


878 


685 


322 


IX-X 


992 


915 


700 


293 


X-XI 


1018 


941 


717 


300 


XI-XII 


1052 


1007 


777 


275 


XII-I 


1137 


1069 


838 


299 


Amplitude 


0-162 


0-234 


0-186 


0-258 


Expectancy 


0-038 


0-039 


0-045 


0-069 








1 



SEMI-ANNUAL PERIODICITY (THREE-MONTHLY SUMMATIONS) 



Month 


T 


T 


T(2Q) 


rw 


I or VII 


1100 


1017 


784 


383 


II or VIII 


1055 


1000 


718 


348 


III or IX 


1081 


981 


768 


312 


IVorX 


1108 


1040 


834 


274 


VorXI 


1153 


1057 


844 


309 


VI or XII 


1127 


1076 


784 


345 


Amplitude 


0-074 


0-075 


0-053 


0-230 


Expectancy 


0-038 


0-039 


0-045 


0-069 



The principal facts to be noted are these : 

1. The last four years give a maximum from two to 
three months later than the other groupings ; they give an 
amplitude distinctly greater than is given by the twenty 
years' grouping ; and the semi-annual periodicity is con- 
siderably increased relatively to the annual periodicity as 
compared with what holds in the other groupings. This 
shows merely that the period is too short to base any con- 
clusions on. And if this is the case for the comparatively 
great frequency in the Tokyo district, it will certainly also be 
the case for districts of less seismicity. We cannot expect 
to get good results from meagre statistics. These always 
give more irregular means, and greater relative amplitudes. 



126 EARTHQUAKE PHENOMENA VII 

2. Comparing the first two groupings, we see that the 
exclusion of the marked numbers in Omori's list greatly 
affects the annual periodicity in amplitude, and brings the 
maximum frequency time about a month earlier. On the 
other hand the semi-annual periodicity is hardly affected 
either in amplitude or in time of maximum. The arbitrary 
exclusion of all the recorded shocks in particular months 
on the ground that the majority are aftershocks of a large 
earthquake in a neighbouring district does not improve 
the numbers as a body of statistics. 

3. The whole twenty-four years of records may be roughly 
divided into two halves, of which the first is characterized by 
a much lower seismicity than the second. Thus from 1876 to 
1887^the records number 738, whereas from 1888 to 1899 they 
run up to 1470, just about double. All were observed 
instrumentally ; and it is stated in the introduction that 
the majority of the seismographs used were of the Gray- 
Milne type. This form of seismograph was not in existence 
as early as 1876, and was not in general use till about 1884. 
There seems to me to be some little uncertainty as to the 
meaning of this great increase of seismicity since 1887. 
Not one single year before that date shows so great a fre- 
quency as 90, and only one year since that date shows 
a smaller, while all the others are marked by a distinctly 
greater frequency. The introduction of more delicate forms 
of seismograph would of course increase the apparent 
frequency. 

I have considered with some care the Tokyo list of shocks, 
which is more complete than any of the others, my aim being 
to come to some understanding as to the certainty with which 
we may draw broad conclusions from records of shocks felt 
but not necessarily originating in limited regions. It is 
very doubtful if we have yet accumulated sufficient material 
to justify any attempts to establish various periodicities in 
the seismic frequency of limited regions. Omori himself 
leaves out of account the returns from certain stations on 
the ground that there are too few shocks. It seems to me 
that he might quite reasonably have drawn the line so as 
to exclude a number of other stations, which have a small 



VII PERIODICITIES 127 

monthly average and a small number of years of observa- 
tions. My own feeling is that the minimum allowable for 
statistical work of this kind is an average of three shocks per 
month over an interval of twelve years. Of the fifteen 
stations of Omori's A group only four stand this test, namely, 
Tokyo, Nagoya, Gifu, and Kumamoto. Gifu and Nagoya 
became seismic centres of importance only after the great 
disaster of October, 1891 ; and the majority of the thousands 
of shocks recorded in the eight succeeding years occurred 
within the first five, being of the nature of aftershocks of 
the great earthquake. In taking the monthly means, how- 
ever, Omori excludes the shocks of 1891, 1892, and 1894, so 
that practically he is dealing with 520 shocks in eight years 
in the case of Nagoya, and 898 shocks in the same time in 
the case of Gifu. The Kumamoto list contains 1578 shocks 
in 10-5 years. The usual substitution of the mean values in 
certain months instead of the recorded number reduces this 
to 746 shocks in ten years. Treating this in the same way 
I find the following results : 

Annual Semi-annual 

Maximum month. III-IV IV and X 

Amplitude 0-32 -079 

Expectancy -065 -065 

Comparing this with S' for Tokyo we see that Kumamoto 
and Tokyo give very similar results. 

Out of the eleven stations of Omori's B group only four 
can be admitted as satisfying the condition laid down above, 
namely, Nemuro, Miyako, Ishinomaki, and Fukushima. 

Nemuro 1343 shocks in 15 years (5 years instrumental) 
Miyako 704 17 

Ishinomaki 1034 14 
Fukushima 857 ,,11 
Utsunomiya 492 9 

the last being just on the margin. Unfortunately even in 
these cases the instrumental observations are for a very 
limited number of years. If we take into account only the 
years of instrumental observations, we find that these 
number 4 in the case of Miyako, nearly 5 for Fukushima, 
6 for Utsunomiya, 9 for Ishinomaki, and 12 for Nemuro. 



128 EARTHQUAKE PHENOMENA VII 

Treating the Nemuro shocks by the method of over- 
lapping sums I find as follows : 

Annual Semi-annual 

Maximum month VII- VIII V and XI 
Amplitude 0-137 0-107 

Expectancy -048 -048 

The true interpretation of this result is that there is no 
clear evidence of an annual periodicity at all. The amplitude 
is comparatively small. 

The cumulative evidence from the statistics of these five 
stations does, however, point towards the conclusion reached 
by Omori, that along the north-east coast of Japan the 
frequency tends to a maximum in the warmer months, 
while in other parts of Japan more frequently visited by 
earthquakes the maximum tends towards the early months 
of the year. We need, however, a larger body of statistics 
to make this conclusion sure, and for this we must wait for 
a sufficient lapse of time. 

Omori points out that the stations of his B group are 
mostly shaken by shocks which have their origins under the 
ocean, whereas the stations of group A are more subject to 
earthquakes having their sources below the land. If and 
Omori adopts this hypothesis also we are to explain the 
winter or spring maximum frequency by the annual baro- 
metric changes, then it seems hopeless to make this also the 
cause of the indicated summer or autumn maximum in 
the case of the stations forming the B group. Both Davison 
and Omori seem, however, to look entirely to the statical 
pressure over the district considered at the time of maximum 
frequency. As already pointed out, we should consider the 
amount of the barometric gradient across the district and 
the changes in that gradient as the year goes on. It must 
be because of the change in distribution that the frequency 
is affected. With no change there would be no changing 
influence upon the seismically sensitive region ; and this 
we must have if there is to be a corresponding periodicity 
in the seismic frequency. The change in distribution may 
be of two kinds. There is first the space change, or gradient, 



VII PERIODICITIES 129 

producing varying loads as we pass across any region of the 
earth's surface, and then there is the time change, which 
means a changing gradient with accompanying changes of 
differential load. These at least are possible dynamical 
causes, not only of an annual, but also of a semi-annual, 
periodicity. 

There are, however, other meteorological phenomena 
which might with reason be expected to influence the seismic 
frequency. There is the accumulation of snow over land 
areas in winter and spring. Also the rate of denudation 
of the uplands and the forming of new deposits along the 
shores will be affected by the periodicity of the rainfall 
and the melting of the snows ; and this, by altering the 
loading, will affect the isostasy of the land masses and 
influence the seismic frequency. It is hardly possible to 
credit the solar radiation with any direct influence ; for, as 
we learnt long ago from the measurements by Forbes of 
underground temperature, solar radiation penetrates a very 
short distance into the earth's crust. 



CHAPTER VIII 

PERIODICITIES (continued) 

Lunar Periodicities. Lunations. Milne's Catalogue of Japanese Earth- 
quakes. Analysed in Terms of Months. Author's Analysis. Ima- 
mura's Later Work. De Ballore's Analysis. Author's Examination 
of Lunar Day Periodicity. Omori's Investigations. Oldham's Dis- 
cussion of Aftershocks of Assam Earthquake. Solar Day Periodicities, 
Davison's Analysis. Omori's Investigation of the Fluctuations in 
Aftershocks. 

IN 1893, Professor Milne published an important catalogue 
of Japanese earthquakes. These, numbering 8331 in all, 
were conveniently arranged according to districts, and I was 
tempted to investigate possible lunar periodicities among 
them. The labour involved in such an investigation is 
considerable, that is, if we are to group the material day by 
day throughout a whole lunar month, and not simply 
according to the moon's quadrantal positions. 

As already stated, Perrey found evidence that earth- 
quakes were more frequent at new moon and full moon 
than at half moon ; more frequent at new moon than at 
full ; more frequent when the moon was in perigee than 
when in apogee ; more frequent at times of meridian passage 
of the moon than at other times. Later discussions along 
Perrey 's lines have not corroborated his conclusions. His 
method was faulty inasmuch as it assumed that the maxi- 
mum, if present, should occur at the lunar times mentioned. 
The only sure way of tracing a possible periodicity is to 
group the earthquakes day by day throughout the whole 
lunar month. If they were grouped even week by week, 
an existing periodicity might quite possibly be masked by 
the process of taking the means in successive weeks. On 
the other hand, by taking overlapping means over a sub- 
multiple of the whole period we are more certain of finding 
an existing periodicity of long period. 



VIII PERIODICITIES 131 

This is the method I adopted in a paper published in 
abstract in the Proceedings of the Royal Society of London 
in 1897, in which I discussed Milne's statistics of 8331 
Japanese earthquakes from 1886 to 1892 inclusive. The 
following extract from the paper will sufficiently explain 
the nature of the investigation into the possible lunar- 
monthly and fortnightly periodicities. 

* There are five distinct kinds of months recognized by 
astronomers, namely : 

(1) The anomalistic month (27-545 days). 

(2) The tropical month (27-322 days). 

(3) The synodic month (29-531 days). 

(4) The sidereal month (27-3228 days). 

(5) The nodical month (27-212 days). 

' Of these, the last two cannot be regarded as having any 
influence on earthquake frequency, for the only conceivable 
effect is a tidal one, and the sidereal and nodical months 
have no necessary tidal relations. At the same time the 
periods of the sidereal and tropical months are so nearly the 
same that they can hardly be discriminated in the lapse of 
eight years. On the other hand, the anomalistic month 
may show itself in earthquake frequency, since the moon 
in perigee has a greater tidal action than when it is in apogee. 
Again, because of the moon's variation in declination, being 
now north of the Equator, now south, we may reasonably 
search for a tropical monthly periodicity. And, finally, 
the synodic or common month may make itself apparent, 
there being possibly a greater tidal stress when the moon 
is in syzygy (as in ordinary spring tides) than when the moon 
is in quadrature (as in neap tides). 

'The earthquakes were accordingly tabulated according 
to these four months, whose periods differ appreciably ; 
the nodical month being also included. For, by analysing 
the statistics in terms of both the tropical and nodical 
months, we may be the better able to draw conclusions as 
to the real existence of one or other periodicity. 

'It should be mentioned . . . that the number of earth- 
quakes which really occurred during the last time interval 
was increased in the proper ratio ; so that the frequency 
during this last interval was made comparable with the 
frequencies of the other intervals. 

' In all cases the obvious aftershocks of any earthquake 
occurring on the same day were neglected. The 3000 after- 
si 2 



132 



EARTHQUAKE PHENOMENA 



VIII 




FIG. 28. LUNAR PERIODICITIES. 
(Reproduced by permission from Proc. Jt.S., 1897. 



VIII 



PERIODICITIES 



133 



shocks of the great disaster of October 28, 1891, were also 
left out. 

' The earthquakes on which the discussion is based numbered 
from 4725 to 4741, the number varying slightly for each 
monthly period, since, at the beginning and end of the 
eight years' interval, there were always a few, differing for 
the different months, which did not make up a complete 
period, and were, consequently, neglected. 

'Each series of numbers was analysed harmonically as 
far as the first four harmonics, &c.' 

The statistics on which the investigation was based were 
not given in the published abstract. They are tabulated in 
the following table, which shows the daily frequency through- 
out each month. 

LUNATION FREQUENCIES 



! Day 


Anomalistic 


Tropical 


Nodical 


Synodic 


1 


153 


183 


150 


168 


2 


152 


198 


182 


173 


3 


174 


173 


166 


176 


4 


155 


188 


156 


169 


5 


204 


220 


213 


139 


6 


157 


150 


180 


145 


7 


168 


183 


203 


142 


8 


186 


163 


176 


177 


9 


196 


158 


187 


170 


10 


180 


130 


162 


155 


11 


179 


172 


186 


155 


12 


173 


185 


188 


160 


13 


151 


176 


190 


174 


14 


178 


164 


184 


157 


15 


182 


189 


153 


176 


16 


185 


155 


164 


158 


17 


181 


166 


147 


161 


18 


174 


179 


134 


184 


19 


188 


157 


148 


149 


20 


150 


156 


186 


181 


21 


175 


184 


167 


158 


22 


175 


164 


181 


134 


23 


176 


177 


170 


168 


24 


183 


166 


181 


133 


25 


165 


170 


180 


143 


26 


163 


181 


196 


148 


27 


131 


192 


166 


161 


28 


178(97) 


190(61) 


170(36) 


173 


29 








1 .1.") 


30 








181(96) 


! Totals 


4731 


4740 


4732 


4725 



134 



EARTHQUAKE PHENOMENA 



VIII 



The number in brackets after the last tabulated frequency 
in each column is the real observed frequency during the 
fraction of the day which completes the corresponding month. 
The bracketed numbers are used in finding the total number 
of shocks. The curves shown in Fig. 28 are smoothed by 
taking overlapping means for five days. 

The statistics were treated by the method of overlap- 
ping summations so as to accentuate the annual monthly 
and half -monthly periodicities. The results are given in 
the following table : 

LUNATION PERIODICITIES 1 



Month 


Day of Maximum 


Amplitude 


Expectancy 


Month 


Half-month 


Month 


Half-month 


Anomalistic 
Tropical 
Nodical . 
Synodic . . 


11-12 

26-27 
8-9 
14 


8 
1 
11 
15 


.0557 
0663 
0602 
0255 


0501 
0551 
0705 
0695 


0258 

?> 


5 



To quote from the paper of 1896, a study of this table 
' discloses the presence of certain features which have no 
raison d'etre on any rational theory of tidal stresses. The 
most important of these is the fact that the nodical month 
(that is, the passage of the moon from node to node), which 
has no direct connexion with tidal stress periodicity, is 
characterized by amplitudes greater on the average than 
those corresponding to the other months '. There is also, 
as Schuster pointed out, the question as to the relative 
magnitudes of the amplitudes and the expectancy or 
probable value of the amplitude if the events were quite 
disconnected and subject to no periodic law. The proba- 

1 I give here in a footnote the table of amplitudes and phases obtained 
from the same set of data by use of Fourier's analysis. The amplitudes are 
relatively very similar ; but the phases differ considerably. 

Amplitudes, c, and Phases, a, of the First Four Harmonics 
Month Ci c Co c 4 o o 2 ^<? ^4 

Anomalistic 46-2 47-8 12-9 16-5 21-7 8-5 5-2 6-2 
Tropical . 54-7 40-7 23-1 17-2 6-0 1-9 7-9 2-4 
Nodical. . 49-5 55-2 28-3 17-6 1-2 7-9 6-9 2-7 
Synodic. . 11-0 52-1 24-5 4-7 13-7 2-7 7-7 06 



VIII PERIODICITIES 135 

bility that the amplitude in such a case should exceed twice 
the expectancy is -0432, or 1 in 23. 

In the course of eight years there are 106 anomalistic 
lunations, 107 tropical, 107-4 nodical, and 98-9 synodic. 
The difference between the tropical and nodical should 
have been sufficient to get rid of a possible ' tropical ' 
periodicity from the statistics when grouped according to 
the nodical month. But the amplitudes are more con- 
spicuous in the nodical than in the tropical grouping. 
There seems to be therefore no distinct evidence of seismic 
frequency being dependent on variation of tidal stress as 
the moon approaches to or recedes from the earth, or as 
the moon passes from south of the equator to north of the 
equator and back again. 

As regards the synodic month, the greatness of the half- 
monthly amplitude as compared with the monthly ampli- 
tude, and the times of occurrence of the maxima and 
minima, lend some support to the view that we have an 
indication of tidal effect. The maxima occur at the times 
of new moon and full moon, just about the times when, in 
virtue of the combined action of sun and moon, the ocean 
tides attain their maxima. 

In No. 18 of the Publications of the (Japanese) Earth- 
quake Investigation Committee (1904), Mr. Imamura has 
discussed in considerable detail the synodic monthly 
periodicities of the seismic frequencies of the same groups 
of earthquakes which Omori had already utilized in his 
work on the annual and semi-annual periodicities. Here 
also in the great majority of cases the statistics are too 
meagre and the lapse of time too short for any certain 
conclusion to be drawn. The method of analysis employed 
by Imamura is identical with that used by Omori, and is 
purely graphical. The shocks are first tabulated in lunar 
days, reckoning from new moon ; and the total synodic 
daily numbers so obtained are plotted on section paper, 
the successive days of the lunar month being laid off hori- 
zontally. The very irregular graph so obtained is then 
smoothed by ' drawing a continuous free-hand line, which 
passes through the mean positions of every two consecutive 



136 EARTHQUAKE PHENOMENA VIII 

points tangentially to the (straight) line connecting directly 
the points themselves '. The varieties of graph are nearly as 
numerous as the places for which they are drawn. In all cases 
there are from ten to fifteen crests and hollows of varying 
amplitudes ; but it cannot be said that there is a tendency 
for the crests of greatest amplitude to occur at the same 
time for even the majority of the stations. For example, 
there is a prominent crest about day 17 in the graphs for 
Nagano, Fukuoka, Niigata, Tokyo, Maebashi, Mito, and 
Nemuro, that is, practically all over the country from the 
extreme south-west to the extreme north-east ; but in the 
graphs for Kagoshima, Gifu, Osaka, Nagoya, Wakayama, 
Aomori, Hikone, Hakodate, Fukushima, and Ishinomaki, 
the prominent crests occur at quite other times . and in three 
important cases there is absolutely no crest at all within 
two days of that date. Imamura considers that he finds 
evidence of the existence of four principal maxima through- 
out the lunar month. Two of these he connects with the 
times of opposition and conjunction of sun and moon ; 
and the other two he connects in a very ingenious, but in 
my opinion very artificial and forced manner with the 
concurrence of the times of daily barometric maximum and 
ordinary high tide. It is obvious that with crests occurring 
on an average every two or three days it is not difficult to 
find four such coming within a day or two of particular dates ; 
and having regard to the meagreness of the statistics in 
most instances, and the doubtful accuracy of the method 
of smoothing, I question if any confidence can be placed 
on the results indicated. To show the danger of the method 
of smoothing I need only refer to the case of Mito, which 
was mentioned above as having a pronounced crest near 
day 18. By a second process of smoothing this prominent 
crest practically disappears, and in one of the tables the 
dates for the four maxima are given as days 6, 14, 26, 
and 30. 

In addition to the graphs for recent earthquakes in the 
individual stations, Imamura gives also the graphs for the 
historic shocks (416 A.D. to 1860 A. D.) of Japan and Kyoto. 
The former catalogue includes 2525 shocks and the latter 



VIII 



PERIODICITIES 



137 



1604. The graphs are fairly similar, showing, after one 
smoothing, pronounced maxima on days 2, 7, 13, and 24. 
The Tokyo graph based on 2464 shocks between 1875 and 
1902 has its maxima falling on the days 7, 18, 23, and 30. 
The maxima on days 7 and 23 agree very well with the 
7 and 24 of the Japan graph ; but these are connected with 
coincidence of causes which, although admissible for a limited 
region like Tokyo, cannot possibly be applied to the whole 
of Japan. It cannot be said that 30 and 18 are in good 
agreement with 2 and 13, there being a difference of three 
days between the first pair and five between the second ; 
and yet these, being by hypothesis due to conjunction of 
sun and moon, ought to be in good agreement aU over the 
country. 

So far as the number of shocks involved are concerned 
the four best catalogues prepared by Imamura are those 
for Tokyo, Gifu, Ishinomaki, and Miyako. These, along 
with the historic list for all Japan, I have submitted to 
the method of overlapping means, and have obtained 
the following results for the assumed monthly and half- 
monthly periodicities.. 

SYNODIC MONTH PERIODICITIES 





No. of 


Day of Maximum 


Amplitude 


Expec- 




Shocks 


Month 


Half-month 


Month 


Half-month 


tancy 


Japan . 
Tokyo . 


2525 
2464 


8 
23 


4 

5 


079 
066 


044 
066 


0354 
0356 


Gifu . . ! 938 


10 


6 


077 


050 


0579 


Ishinomaki 


1307 


19 


13 


112 


065 


049 


Miyako . 


923 


3 


10 


126 


137 

- 


0583 



With the view of testing directly the suggested existence 
of four maxima at times of conjunction and times of quad- 
rature, I divided Imamura's numbers for Tokyo into half- 
monthly sets, making sixty in all. These were then divided 
into four groups of 15 each, and finally combined into one 
resultant set of 15, each member of this resultant set being 
the sum of the four numbers occupying the corresponding 
places in the initial groups. This final group was then 
subjected to the usual treatment by overlapping summa- 



138 EARTHQUAKE PHENOMENA VIII 

tions so as to emphasize the period of 7-5 days. The 
maximum came out about the end of the second day, recur- 
ring of course at intervals of 7-5 days thereafter. The 
corrected amplitude was 0-038, which is very slightly greater 
than the expectancy. The times of maxima indicated by 
this method of analysis, namely, 2-5, 10, 17-5, and 25, do 
not agree particularly well with Imamura's deductions from 
the smoothed graphs, namely, 30, 7, 18, 23. The evidence 
in favour of the existence of a quarter-monthly periodicity 
seems to be much more precarious than the evidence in 
favour of the existence of the longer associated perio- 
dicities. 

If we take along with these five sets of statistics the set 
prepared by myself from Milne's catalogue, we find very 
little harmony among them. There is absolutely no agree- 
ment in the times of the maximum frequencies either for 
the monthly or half -monthly periodicities. The amplitudes 
are no doubt of the same order of magnitude, but in 110 
case more than three times the expectancy. In Imamura's 
statistics there is no indication of the pronounced half- 
monthly amplitude which was characteristic of the larger 
mass of statistics used by me. On the whole we are driven 
to the conclusion that the reality of a tidal periodicity in 
earthquake periodicity due to the action of the moon is 
still unproved. 

We pass now to the consideration of periodicities of 
comparatively short period, namely, the lunar and solar 
days. Let us consider the lunar day first. 

Perrey concluded from his statistics that earthquakes 
were more frequent at times of meridian passage of the 
moon than at other times. No serious attempt was made 
to test this conclusion with the increased and yearly in- 
creasing material to hand till 1889, when de Ballore with 
his catalogue of nearly 45,000 shocks found no clear evidence 
at all for a lunar daily periodicity. Dividing the whole 
lunar day of 24 h. 50m. into eight parts, of which the middle 
of the first part corresponds to the time of the superior 
culmination, he found the following grand total of earth- 
quake distributions : 



VIII PERIODICITIES 139 

Eighths I II III IV V VI VII VIH 

Earthquakes 5579 5558 5611 5508 5802 5564 5571 5662 
If we treat these by the method of overlapping sums so 
as to separate out the daily and half-daily periods we find 
the daily maximum to fall exactly at the time of the lower 
culmination, and the half -daily maxima at the times very 
slightly preceding the times of the superior and inferior 
culminations. The corrected amplitude comes out 0-0125 
for the daily period and 0-01 for the half-daily, while 
Schuster's expectancy for an equal number of random 
events is -0084. The probability that the amplitude for 
the random events should exceed 0-0125 is 0-172 or about 
1 in 6. If we accept the result as evidence that the daily 
tidal stress due to the moon has an influence on seismic 
frequency the effect is very slight. 

In the paper on Lunar Periodicities already referred to 
I discussed also the lunar daily period in the statistics 
afforded by Milne's catalogue of Japanese earthquakes. 
The earthquakes in each of the fifteen districts into which 
Milne divided the country were tabulated in quarter-hour 
intervals after meridian passage of the moon. The statis- 
tics for the ten groups into which for convenience the fifteen 
were arranged were then discussed separately by Fourier's 
analysis as far as the fourth harmonic. In all but Districts 
6 and 7 the numbers of shocks on which the discussion was 
based were too small to yield trustworthy results. This 
was shown by the largeness of the amplitudes as compared 
with the amplitudes furnished by the statistics for Districts 
6 and 7. 

Here we shall confine our attention entirely to the 
statistics of the two districts named, and the following 
table gives the data tabulated in quarter-hours throughout 
the lunar day. 

We may call District 6 the Tokyo district, and District 7 
the Nagoya district. The latter did not become promi- 
nently seismic till after the great shock of 1891. 

In Fig. 28 (p. 132) smoothed curves of the lunar daily 
periods are shown for Districts 6 and 7, and for all 
combined. 



140 



EARTHQUAKE PHENOMENA 



VIII 



Hour 


Tokyo District 


1 


19 11 


18 17 


2 


10 17 


9 21 


3 


13 17 


20 12 


4 


13 18 


6 8 


5 


15 19 


15 16 


6 


19 6 


11 14 


7 


12 11 


13 11 


8 


18 24 


24 13 


9 


6 25 


18 16 


10 


6 20 


12 11 


11 


21 12 


9 12 


12 


17 10 


12 13 


13 


12 18 


13 17 


14 


16 17 


20 12 


15 


12 10 


10 17 


16 


13 14 


16 22 


17 


11 14 


20 14 


18 


14 19 


16 15 


19 


13 15 


10 15 


20 


11 11 


10 16 


21 


18 11 


11 19 


22 


13 20 


17 4 


23 


9 12 


19 10 


24 


15 8 


16 14 


25 


17 23 


10 13 




Total 


1432 



Nagoya 


District 


29 


37 


43 


33 


44 


34 


41 


49 


28 


45 


33 


38 


30 


41 


29 


39 


30 


22 


39 


38 


38 


31 


40 


43 


28 


30 


37 


35 


34 


46 


39 


42 


46 


29 


34 


39 


41 


38 


30 


19 


28 


45 


33 


44 


39 


31 


33 


34 


28 


47 


35 


36 


31 


35 


32 


42 


35 


37 


37 


32 


36 


30 


33 


43 


42 


36 


33 


34 


36 


31 


37 


40 


40 


36 


30 


42 


37 


40 


41 


41 


38 


38 


44 


37 


42 


33 


34 


37 


34 


43 


37 


40 


39 


41 


34 


31 


31 


32 


44 


25 


3632 



From these numbers we may by suitable grouping and 
taking of overlapping sums deduce the daily, half-daily, and 
quarter-daily periodicities. They are as follows : 



Lunar Day 


Amplitude 


Hour of Maximum 
after culmination 


Tokyo 


Nagoya 


Tokyo 


Nagoya 


Whole . . 
Half . . . 
Quarter . . 
Expectancy 


0-048 
0-062 
0-059 
0-047 


0-029 
0-045 
0-055 
0-029 


12 
2-3 
3 


22 

8 
2 



The times of maximum are quite different in the two 
cases, although the two districts do not lie very far from 
each other. It is not easy to see why there should be 
such a marked difference if there be anything of the nature 
of a tidal stress affecting the seismic frequency. Moreover, 
in accordance with Schuster's criticism the amplitudes are 
for the daily periodicity almost identical with the expect- 



VIII 



PERIODICITIES 



141 



ancy for haphazard events. There is consequently no 
evidence of a lunar daily period. The half and quarter- 
daily amplitudes are somewhat larger; and the fact that 
this occurs in both sets of statistics may be regarded as 
hinting at the possibility of such a periodicity ; but clearly 
we have not yet accumulated a sufficient amount of material 
over a limited region of the earth to warrant us in drawing 
any but a negative conclusion. 

Omori has studied the daily lunar period in connexion 
with the earthquake frequencies at Nagoya, Nemuro, and 
Tokyo, the number of shocks and interval of time being as 
follows : 

Nagoya 1270 earthquakes from 1891 to 1899 
Nemuro 799 1894 to 1899 

Tokyo 1462 1888 to 1899 

Treating the numbers by the method of overlapping 
sums I find the following results for the times of the lunar 
daily, half -daily, and quarter-daily maxima, and for the 
corresponding corrected amplitudes. The reckoning is 
from upper culmination : 





Nagoya 


Nemuro 


Tokyo 


All 


All (Solar) 


Daily max. 
Half -daily max. . 
Quarter-daily max. 

Daily 


Hour 
7-5 
3-5 
4 

Amp. 
0-095 


Hour 
7-5 
2-5 
1-5 

Amp. 
0-065 


Hour 
10-5 
3-5 
5-5 

Amp. 
0-016 


Hour 
7-5 
3-5 
3 

Amp. 

0-048 


Hour 
3-5 
2-5 
5 

Amp. 
0-081 


Half -daily. . . . 
Quarter-daily 
Expectancy . 


0-112 
0-05 
0-05 


0-095 
0-013 
0-063 


0-032 
0-067 
0-046 


0-081 
0-017 
0-03 


0-016 
0-05 
0-03 



These results do not at all agree with the conclusions 
arrived at by Omori, who does not work with overlapping 
means, but seems to assume that the hour with the greatest 
observed frequency is the hour of maximum frequency. 
But this could only be true when a very great number of 
shocks were taken into account. Omori considers also what 
he calls three-hourly distributions. The frequencies for 
the hour intervals 1-3, 4-6, 0-3, 3-6, 6-9, 9-12, 12-15, 
15-18, 18-21, 21-24, are added together forming eight 



142 EARTHQUAKE PHENOMENA VIII 

separate summations, and these are then considered as 
indicating certain periodicities. The fallacy of this method 
lies in the fact that there is no reason why this particular 
grouping should be chosen instead of any other similar 
grouping, such as, for example, 2-5, 5-8, 8-11, and so on 
to the last 23-2. But when this is done it will be found 
that in the case (to take simply the first) of Nagoya, the 
principal minimum number of this three-hourly distribution 
falls between the 17th and 20th hours instead of the 21st 
and 24th hours according to the distribution used by Omori. 
The truth is that any arbitrary method of partitioning 
the numbers in separate and non-overlapping subgroups 
may very easily be such as to mask a real periodicity instead 
of accentuating it relatively to other possible periodicities. 

On the other hand, if there be any real daily, half-daily, 
or quarter-daily periodicity present, the method of taking 
overlapping sums over suitable intervals cannot fail to 
bring them into evidence. In the present condition of 
earthquake statistics this seems to me to be the only reason- 
able method for testing the existence of possible periodicities. 
The labour involved in applying the Fourier analysis to 
insufficient statistics is a sheer waste of time. 

Let us now examine the results as a whole. The first 
point to notice is the tendency for the relative amplitudes 
to diminish as the statistical number increases. This shows 
that no reliance can be placed on the values of amplitudes 
unless the number of shocks is very great greater than 
any of the individual cases discussed by Omori, Imamura, 
or myself. Taking into account de Ballore's much larger 
body of statistics, the only result on which most of the cases 
agree is the tendency for the half-daily maxima to occur 
in the neighbourhood of times of culmination. This might 
be considered as due to the daily tidal stress of the moon. 

The last column of the table on p. 141 gives correspond- 
ing results for the solar instead of the lunar day. They are 
inserted for the sake of comparison and will be referred to 
further on, when the question of the solar day is con- 
sidered. 

The lunar day periodicity has been considered in a novel 



VIII 



PERIODICITIES 



143 



way by R. D. Oldham with reference to the aftershocks of the 
great Assam earthquake of June 12, 1897. 1 An interesting 
discussion is given of the character of the tidal stresses 
produced by sun and moon as it is influenced by the declina- 
tion of these bodies. This leads to the grouping of the 
statistics in three sets according as the declination is greater 
than 9N., lies between 9N. and 9S., or is greater numeri- 
cally than 9 S. The grouping is effected with reference 
both to the lunar and the solar day. The lunar day is 
taken as equal to 25 mean solar hours, an appropriate 
correction being applied to the frequency as obtained for 
the last hour. Unfortunately it is not possible to apply 
at once the method used systematically throughout this 
chapter to statistics which are arranged in an odd number 
of groups. Accordingly I have slightly readjusted the 
numbers given so as to arrange them in 24 groups, increas- 
ing the numbers as given by Oldham by a suitable pro- 
portion, but so as to leave the whole number of earthquakes 
the same. The method may be open to criticism, but the 
rearrangement so deduced cannot differ appreciably from 
what would have been obtained had the statistics been 
arranged de novo in groups of 24 to the lunar day. Applying 
to this rearrangement and to the solar-day statistics the 
method of overlapping sums I obtained the two following 
tables of results. The solar day periodicity is to be con- 
sidered in the succeeding paragraphs ; but it is convenient 
to give the two arrangements of the same set of statistics 
together so that they may be easily compared. 

LUNAR DAY PERIODICITIES 



Declination 


Number of 
earthquakes 


Day 


Half-Day 


Quarter- 
Day 


Expectancy 


9N.+ 
9N. to9S. 

9S.+ 
All 


510 
333 
431 
1274 


18 h. 
099 
18 h. 
147 
24 h. 
202 
20 h. 
062 


4h. 
099 
8h. 
308 
Ih. 
128 
8h. 
05 


3-5 h. 
099 
5-5 h. 
099 
0-5 h. 
113 
1-5 h. 
0-4 


078 
097 
085 
05 



1 See Memoirs of the Geological Survey of India, vol. xxxv, part 2. 



144 



EARTHQUAKE PHENOMENA 



VIII 



SOLAR DAY PERIODICITIES 



Declination 


Number of 
earthquakes 


9N.+ 


436 


9 N. to 9 S. 


358 


9S.+ 


480 


All 


1274 



Day Half-Day 

17 h. 9h. 

137 -152 

18-5 h. 6h. 

132 -132 

1 h. 5 h. 

335 -118 

! 9h. 

177 -076 



Ih. 



Quarter- 
Day 


Expectancy 


4h. 
137 
4-5 h. 
255 
5-5 h. 
092 
4-5 h. 
144 


083 
094 
, -087 
05 



The first column gives the declination of the tide-producing 
body ; the second the number of earthquakes ; and the 
last column the expectancy. The third, fourth, and fifth 
columns contain the phases and amplitudes calculated in 
the way used throughout the chapter. The number entered 
in the phase sub-column is the time of maximum reckoning 
from the lower culmination of the tide-producing body, that 
is, from midnight in the case of the solar day, and from 
what might be called mid-lunar-night in the other case. 

From theoretical considerations Oldham was led to look 
for maximum frequency about the time of higher culmina- 
tion when the influencing body was well to the north of 
the equator and about the time of lower culmination when 
the body was well to the south of the equator. There is 
some hint of this in both tables ; but the evidence of the 
amplitude is not reassuring. For example, if the moon's 
tidal stress were to have any influence, we should expect 
to find the amplitudes as large for declinations greater 
than 9 N. as for declinations greater than 9 S. Not only 
is this not the case but the values of the amplitudes in 
most cases are not much greater than the expectancies. 
Although it must be admitted that the results so far are 
negative, nevertheless the point of view which led Oldham 
to discriminate between cases according to the declination 
is one deserving of more attention. It emphasizes the 
possibility, already referred to in other connexions, that in 
an indiscriminate grouping according to probable periodici- 
ties there may be a balancing of effects, so that the periodic 
change looked for may escape notice. 



VIII PERIODICITIES 145 

The idea that earthquakes happen more often during 
the night than during the day is pretty general in earth- 
quake countries. From his investigations in 'Japan Milne 
early came to the conclusion that the apparent preponder- 
ance of night over day shocks was really a personal equation 
of the observers, who are better able to appreciate a moderate 
earthquake during the still night than during the noisy day. 
Instrumental records declared no night maximum. 

In his paper of 1889 already referred to M. de Ballore 
considered the question as to how far his statistics of 45,000 
earthquakes lent support to the hypothesis of a diurnal 
period in seismic frequency. I quote from an abstract of 
his paper which I prepared for the Seismological Society 
of Japan (see Trans. S. S. J., 1890). 

' In five of the seven groups into which, for sound scien- 
tific reasons, he divided the shaken regions, the numbers 
and curves alike showed a night maximum and a day 
minimum. The grand mean for the first six groups, in- 
cluding 37,511 earthquakes, showed that the ratio of the 
day to the night earthquakes was as 8:10. By far the 
great majority of these earthquakes were not instrumental^ 
recorded ; so that the problem was really as much one of 
human sensitiveness to seismic influence as one of earth- 
quake frequency. M. de Ballore concluded in fact that 
this ratio of 8 to 10 represented the relative loss of day 
earthquakes caused by the physiological conditions of 
human activity. 

' In Group VII, which was excluded in the above grand 
mean, a distinct preponderance of day earthquakes was 
shown. But Group VII consisted of the Italian geody- 
namic stations, at which delicate self-recording seismo- 
graphs were in use, working day and night. A large number 
of small tremors were registered, in which real seismic 
disturbances were probably mingled with motions due to 
human operations. Separating out the smallest disturb- 
ances, those namely of Grade I on the Rossi-Forel scale of 
intensities, we get a marked diminution in the apparent 
day preponderancy. 

' Then, again, an instructive corroboration of the con- 
clusion given above was obtained by a discussion of the 
earthquakes in intensity groups. These are ten in number, 
according to the Rossi-Forel conventional scale ; No. I^being 
the small instrumental ones just mentioned, and No. X 



146 EARTHQUAKE PHENOMENA VIII 

being disasters. The ratios of the day and night earth- 
quakes for the different intensities were as follows : 

Intensity I II III IV V VI VII VIII IX X 
Ratio of day 

to night 1-8 -73 -60 -67 -65 -76 -81 -85 1-27 1-02 

' Thus we see at a glance that it is for Intensities III, 
IV, and V, that the night maximum is specially obvious. 
Now these intensities are just the intensities that would be 
apt to be missed during the noisy day. The apparent day 
maximum for earthquakes of Intensity I has been already 
explained these being all registered by delicate seismo- 
graphs. In the higher intensities there is a tendency to 
equality just as we should expect, since emphatic earth- 
quakes will be as evident during the day as during the night. 

' So far, then, we have no evidence in support of the 
somewhat prevalent notion that earthquakes love the 
darkness rather than the light.' 

This dichotomous division of shocks into day and night 
groups does not, however, dispose of the question as to the 
existence of a diurnal periodicity. For this purpose we 
must arrange the shocks in small time intervals, most 
conveniently in hours, and then discuss the statistics in 
some systematic manner. 

In an important paper on the Aftershocks of Earthquakes, 1 
Omori has grouped certain sets of shocks in hour intervals 
with the view of testing any existing periodicity. The 
results were represented graphically, and the graphs were 
smoothed apparently by the same process as that subse- 
quently used by him in treating of the annual and lunar 
monthly periodicities. The method is somewhat arbitrary 
and leads to no true numerical relation among the ampli- 
tudes or phases of the possible periodicities. 

In a paper published in the Philosophical Magazine (1896) 
Dr. Davison applied harmonic analysis to certain earth- 
quake statistics, carrying the determination of the con- 
stituents as far as the sixth harmonic. 

For the sake of uniformity I propose to discuss by the 
much simpler method of overlapping sums some of the 
statistics already discussed by Omori and Davison. It is 

1 Journal of the College of Science, Imperial University, Japan, vol. vii,. 
1894. 



VIII 



PERIODICITIES 



147 



not necessary here to reproduce the statistics of all the 
cases treated ; but to show their nature it will suffice to 
give two or three extreme cases. The number of shocks 
in each hour interval is entered in the column headed by 
the corresponding hour. The first row in each case refers 
to a.m. and the second row to p.m. In the subsequent 
discussion the day is reckoned from midnight and 1 p.m. 
is called 13 and so on. 



Hour 


0-1 


1-2 ! 2-3 


3-4 


4-5 


5-6 


6-7 


7-8 


8-9 


9-10 


10-11 


11-12 




District 






| 


















Italy 


264|238 264 


250 


248 


257 


260 308 


407 


482 


527 


436 


a.m. 


1872-87 


452 


388 443 


454 


385 


347 


294 


276 


346 


318 


286 


247 


p.m. 


Japan 


133 


153 211 


176 


139 


166 


153 


162 


151 


157 


139 


155 


a.m. 


1885-90 


151 


186 188 


162 


144 


132 


135 156 


153 


184 


185 


171 


p.m. 


Gifu 


56 


64 58 


62 


92 


63 


47 53 


49 


41 


42 


58 


a.m. 


13 days 


54 


48 38 


36 


36 


47 


51 


77 


58 


51 


42 


35 


p.m. 


1891 


























Kurnamoto 


7 


13 18 


12 


11 


11 


3 


6 


4 


2 


4 


3 


a.m. 


14 days 


11 


5 2 


1 


4 


3 


8 4 


5 


2 


4 


5 


p.m. 


1899 




i 








i 













The Italian numbers refer to tremors recorded on Tromo- 
meters ; and probably mechanical tremors due to traffic 
may be mixed up with true seismic tremors. This would 
tend to increase during the day. The Japan list contains 
instrumentally observed earthquakes of small intensity. 
The Gifu numbers are the aftershocks for a fortnight after 
the great Mino-Owari earthquake of October 28, 1891 ; and 
the Kumamoto numbers are aftershocks of the earthquake 
of July 28, 1889. 

It is evident at a glance that these several groups have 
very different claims upon our attention. The inadequacy 
of meagre statistics in a limited region to serve as a basis 
for calculation will be apparent in the results now to be 
given. Although I have no belief in the reality of an eight- 
hours period I have worked out the phase and amplitude 
for this period and for an assumed four-hours period as well 
as for the day, half-day, and quarter-day, the reasons 
being (1) because Omori lays a good deal of emphasis on 

L2 



148 



EARTHQUAKE PHENOMENA 



VIII 



the existence of the eight-hours period, (2) because, in my 
opinion, a large eight-hours amplitude proves the insuffi- 
ciency of the statistics to establish any frequency. 

The eight-hours period was investigated by the same 
method as that used for the half-daily and quarter-daily 
periods. The statistics were arranged in groups of eight 
hours. That is, hours 1, 9, 17 were taken together ; also 2, 10, 
18 ; 3, 11, 19 ; and so on. The numbers so obtained were 
then discussed by taking overlapping sums over four hours. 

The results are shown in the following table. The first 
column contains the names of the countries or districts, the 
second the number of shocks, and the third the expectancy. 
The five remaining pairs of columns give the amplitudes and 
the phases or times of maximum for the various periodicities 
considered. Only the earliest hour of maximum is entered for 
the higher periodicities. In the first column the interval of 
time through which the statistics were taken is also given. 

AMPLITUDES AND PHASES OF ASSUMED DAILY AND SUB-DAILY PERIODICITIES 



District 


Number 
of Shocks 


Expectancy 


24-hours 


12-hours 


6-hours 


8-hours 


4-hours 


Italy 


8177 


0-02 


0-130 


0-118 


0-129 


0-05 


0-019 


1872-87 






13 h. 


11 h. 


3h. 


Ih. 


Ih. 


Japan 


3842 


0-029 


0-054 


0-076 


0-098 


0-065 


0-018 


1885-90 






2h. 


2h. 


25 h. 


6h. 


3h. 


Tokyo 


1168 


0-052 


0-137 


0-059 


0-115 


0-142 


0-037 


1876-91 






18 h. 


10 h. 


3h. 


6h. 


Ih. 


Gifu 


1258 


0-050 


0-206 


0-106 


0-062 


0-219 


0-11 


13 days 






24 h. 


6h. 


Ih. 


4h. 


4h. 


1891 
















Nagoya 


572 


0-074 


0-35 


0-19 


0-049 


0-13 


0-18 


13 days 






3h. 


3h. 


2h. 


2h. 


4h. 


1891 






















22 










Chiran 


233 


0-116 


0-16 


0-164 


0-164 


0-097 


0-25 


5 months 






4h. 


4h. 


2h. 


3h. 


2h. 


1893-4 
















Kumamoto 


148 


0-146 


0-51 


0-52 


0-279 


0-435 


0-088 


1 month 






2h. 


3h. 


Ih. 


4h. 


Ih. 


1889 
















Manila 


208 


0-123 


0-32 


0-19 


0-34 


0-211 


0-14 


1869-89 






11 h. 


3h. 


5h. 


7h. 


Ih. 



VIII PERIODICITIES 149 

A comparison of the amplitudes with Schuster's ' expect- 
ancy ' brings out some interesting points. In the case of 
-Italy with its 8177 shocks the daily, half -daily, and quarter- 
daily amplitudes are all comparatively large, and to that 
extent support the hypothesis of a true solar daily period. 
On the other hand, the eight-hours and four-hours perio- 
dicities show small amplitudes, as on general grounds we 
should expect. The comparative smallness of these two 
amplitudes is not, however, shown in the other cases, at any 
rate so distinctly. It is important to note that when "the 
values of the expectancy are large the amplitudes, though 
in most cases somewhat larger, are not markedly so. This 
would indicate that the statistics are too meagre to establish 
the existence of the daily period. The amplitudes for the 
Italian and Tokyo statistics are respectively 0-13 and 
0-137 ; and the fact that a smaller body of statistics, as in 
the four last cases, is associated with a distinctly larger 
amplitude simply shows that the statistics are not numerous 
enough. In fact the expectancy in the cases of Chiran, 
Kumamoto, and Manila, is practically equal to the ampli- 
tudes which are given by the fuller statistics of Italy and 
Tokyo. Where the statistics are limited the haphazard law 
masks the true periodicity which is being searched for. 

Where comparison is possible the results agree sufficiently 
well with the results given by Davison, at least as regards 
the phases of the assumed periodicities. With the material 
grouped in hour intervals we cannot look for any great 
accuracy in the determination of the times of maximum 
to within half-an-hour perhaps but no nearer. Davison 
gives his phases or epochs to minutes, but that is a refine- 
ment quite beyond the possibilities of the investigation. 

The Japan group of shocks from 1885 to 1890 is taken 
from Omori's list. The group analysed by Davison was 
compiled from Milne's great catalogue, and covers the 
same period. It includes only 1175 shocks, whereas Omori's 
list includes 3842. There must be included in the latter 
list a great many small shocks. Davison finds for the 
times of maximum in the daily, half-daily, third-daily, and 
fourth-daily harmonic the following values : noon, 9 a.m., 



150 



EARTHQUAKE PHENOMENA 



VIII 



6.5 a.m., and 2.5 a.m. ; while my values for the corre- 
sponding quantities as given by Omori's larger list are 
2 a.m., noon, 6 a.m., and 3.5 a.m. There is agreement in 
one case only and that is the eight-hours periodicity, for 
the existence of which there is absolutely no physical basis. 
The daily and half-daily periodicities are quite different. 

Again, if there were any demonstrable reality in the 
daily and half -daily periodicities w r e should expect Gifu and 
Nagoya to give similar results ; for both are in the same 
seismic district and were subject to the aftershocks of the 
same great earthquake. But they differ emphatically until 
we reach the four-hours periodicity, of which also there is 
absolutely no imaginable physical cause. The Gifu shocks 
show a marked eight-hours period ; the Nagoya shocks 
show practicaUy none. This merely means that within the 
short compass of thirteen days certain marked irregularities 
occurred so as to bring out an eight-hours period. Indeed 
a close examination of Omori's list of Gifu aftershocks 
reveals the fact that this eight-hours period is determined 
by the first three of the thirteen complete days for which 
the statistics are given, and to a very great extent by the 
first of these three. The table of Gifu shocks arranged 
according to day and hour is given below (p. 152) mainly for 
another purpose ; and a glance will suffice to show how 
important in shaping the character of the whole is the 
distribution during the early days. 

To make the argument more complete I have separated 
out the statistics into two groups, the first containing the 
627 of October 29, 30, and 31, the second the remaining 
631 during the first ten days of November. Treating the 
data by the same method of overlapping sums I find the 
times of maximum and the reduced amplitudes as follows : 





24-hours 


12-hours 


6-hours 


8-hours 


4-hours 


Oct. 29-31 
Nov. 1-10 


h. 7 
30 
h. 1 
21 


3 or 6 
22 
8 
11 


1-5, 7-5, &c. 
061 
1-5, &c. 
11 


4, 12, 20 

43 
5, 13, 21 

048 


4, 8, 12, c. 
26 
2, 6, 10, &c. 
053 



Expectancy = -071 



VIII PERIODICITIES 151 

Thus the eight-hours period which is so conspicuous in 
the statistics of the first three days, having an amplitude 
greater than that of even the daily or half -daily periodicity, 
is practically non-existent in the statistics of the last ten 
days, its amplitude being only one quarter of that of the 
daily period and one half that of the half-daily, and being 
besides less than the expectancy. Moreover, the times of 
the occurrence of the maxima in the daily and half -daily 
periodicities are quite different in the two cases and differ 
also from the corresponding quantities when the statistics 
are treated as a whole. In short, we can base upon these 
results no conclusions whatever. The data are too meagre. 

The times of the daily maximum for the four stations 
Gifu, Nagoya, Chiran, and Kumamoto, all of which deal 
with aftershocks, occur within four hours of midnight, and 
one of the half-daily maxima occurs about the same time. 
This might have been accepted as evidence ^of a direct 
tidal action due to the sun ; but unfortunately the same 
result is not given by the Italian shocks and by the Tokyo 
group analysed above. The Japan group given in the 
table agrees fairly well with the aftershock groups ; but 
against this we must set Davison's analysis of another 
Japan group. The combined group of Nagoya, Nemuro, 
and Tokyo given in the table on p. 141 shows a diurnal 
and semi-diurnal periodicity in tolerable agreement also 
with the Japan group of the last table, but not at all in 
agreement with the Tokyo group. The evidence is, in 
short, distinctly conflicting ; and it is very doubtful if we 
can place any reliance on conclusions (1) as to the existence 
of a periodicity connected with the succession of day and 
night. (2) as to the times of occurrence of maximum and 
minimum frequencies. 

At Milne's suggestion Omori undertook the first syste- 
matic examination into the law of aftershocks of great 
earthquakes. 1 A good example is the case of Gifu, a town 
in the district of Japan visited by the disaster of 1 891. The 
following table, reproduced from Omori's memoir, shows the 
hourly distribution for thirteen days after the earthquake. 

1 See Introduction to Milne's 'Catalogue of 8331 Earthquakes,' Seismo- 
logical Journal of Japan, vol. iv, 1895. 



152 



EARTHQUAKE PHENOMENA 



VIII 



HOURLY NUMBERS OF EARTHQUAKES AT GIFU FROM OCTOBER 29 TO 
NOVEMBER 10, 1891 





October 


November 




Hour 


28 29 30 31 


123456789 10 


Sum 


a.m. 
0- 1 


9 13 1 


79241252 1 


56 


1-2 


19 12 


9126321243 


64 


2-3 


15 6 10 


941323 113 


58 


3-4 


13 20 5 


1732331 21 


61 


4-5 


25 20 12 


366217226 


92 


5-6 


15 8 13 


4234431222 


63 


6-7 


427 


7235224153! 47 


7-8 


14 5 6 


4452312313 


53 


8-9 


14 9 7 


21522 3211 


49 


9-10 


944 


2425322112 


41 


10-11 


12 3 3 


633411 411 


42 


11-12 


22 7 3 


4343231312 


58 


p.m. 








0-1 


26 5 3 


143316 11 


54 


1-2 


17 10 3 


34331211 


48 


2-3 


11 8 2 3 


262314412 


38 


3-4 


10 9 2 5 


4232231 21 


36 


4-5 


16 11 6 4 


2341 122 


36 


5-6 


3 11 4 2 


4242443124 


47 


6-7 


15 15 5 7 


7232321211 


51 


7-8 


13 16 12 11 


5965251113 


77 


8-9 


9 12 11 6 


34534333 1 


58 


9-10 


11 9 5 2 


8444414132 


51 


10-11 


6 10 1 6 


2434231222 


42 


11-12 


7313 


224253523 


35 


Sum 


101 318 173 126 


99 92 81 78 53 67 45 42 43 40 


1257 



Before the great earthquake the seismic frequency at Gifu 
was normally less than 20 per month, so that the numerous 
individual shocks here recorded are part of the same seismic 
phenomenon, of which the disastrous earthquake was the 
most conspicuous feature. The relief of strain which is 
the real origin of the shock does not establish a state of 
complete equilibrium. A great fault slip, such for example 
as gave rise to the Assam earthquake of 1897 or the San 
Francisco earthquake of 1906, might over-rush the position 
of greatest stability, or it might not quite reach it. A suc- 
cession of smaller slips would necessarily follow, giving rise 
to the so-called aftershocks. Strictly speaking, these after- 
shocks are as much part of the whole phenomenon as the 
great disastrous shock which made the phenomenon historic. 



VIII PERIODICITIES 153 

In many cases the large shock is worked up to by a series 
of preliminary but much smaller shocks. These are recog- 
nized as preliminary only after the great earthquake has 
come and gone. The dynamical problem is then one of 
a kind of which we have many illustrations in molecular 
physics. Because of the action of external forces a state 
of strain is induced in the material tending to a con- 
dition of instability. Yielding or rupture occurs and the 
fractured material takes up a less unstable grouping. Smaller 
yieldings follow until a fairly steady state of equilibrium is 
reached. This will continue for a greater or smaller interval 
of time until the forces work up a new state of instability. 
Another seismic disturbance follows, to be succeeded by 
a sufficient but still temporary state of stability ; and so 
on at uncertain intervals of thirty to sixty years. The 
moderate earthquakes are no doubt subject to similar laws ; 
but their aftershocks are too feeble to be distinguished from 
the ordinary small disturbances which are felt in seismic 
regions. 

It is reasonable to suppose that many small yieldings to 
strain will occur near the seismic focus, but in such a way 
as not to produce any noticeable effect at the surface. 
What we have to deal with are the more intense changes 
which crop out at the surface as sounds or slight move- 
ments. Our records, even with the aid of instruments, can 
never be complete. We obtain but an indication of the 
life history of a complex of seismic disturbances which 
reach more or less abruptly their greatest intensity during 
a brief interval of a few minutes. Thereafter a rapid 
decay of frequency and intensity occurs, dwindling away 
with fluctuations through days, months, and years. Such 
decay is usually expressible mathematically by what is 
called an exponential function of the time ; but Omori 
has shown by trial that it, may in most cases be represented 
by a simple formula of the form 



~ B + t 
where / is the average frequency reckoned over a certain 



154 EARTHQUAKE PHENOMENA VIII 

chosen interval, t is the time from the occurrence of the 
earthquake, and A and B are constants to be determined 
for each case. 

For example, by taking the half -daily frequencies from 
the table just given for Gifu and reckoning from the first 
half of October 29, Omori finds that the formula 

440-7 



2-31 

represents fairly well the half -daily frequencies, not only 
throughout the interval covered by the table, but during 
several succeeding years. Here t is measured in half -days 
reckoning from 6 a.m. of October 29, and indicates the 
middle of the half -day over which / is the frequency. 

Omori has also shown that the relative intensities of 
earthquakes may be compared by the frequencies of their 
aftershocks. 

The decay in frequency of aftershocks is always subject 
to fluctuations, and we have already seen that there is 
some evidence of a daily fluctuation having a maximum 
within a few hours of midnight. As regards annual fluctua- 
tions the nature of the statistics of aftershocks hardly 
allows any conclusion to be drawn. The number of years 
is much too limited ; and the character of the month by 
month variation of frequency is largely determined by 
what happens in the early months immediately succeeding 
the great earthquake. We have seen above how the hourly 
statistics for the first few days stamp their character upon 
the whole body of statistics for thirteen days so as to bring 
into prominence a so-called eight-hours periodicity. A pro- 
minent disturbance or series of disturbances occurring in 
the early months after a great shock cannot fail to impress 
itself on the body of statistics of aftershocks ; and any 
irregular series of numbers arranged in months and then 
in years will show maximum and minimum points. To 
ascribe to these more than a casual nature is, I am afraid, 
impossible in the circumstances. 

By smoothing off the graphical representation of the 
time variation of aftershocks Omori finds evidence of certain 



VIII PERIODICITIES 155 

longer periods than months or years. To account for these 
fluctuations in terms either of tidal action of sun and moon 
or of barometric variations of pressure seems to be out of 
the question ; and we are driven to accept these fluctua- 
tions as being a part of the character of the disturbance 
just as much as the great movement which works havoc 
is a part of it. Periodicity of an irregular kind there is ; 
a periodicity which shows itself in the irregular waves of 
varying intensity which make up every strong or moderate 
shock, and which continues to show itself in the fluctuations 
of intensity as the seismic phenomenon works out its life 
history in a gradual decay. So far as present evidence 
goes these fluctuations are part of the phenomenon and 
depend very slightly if at all upon external influences such 
as might be referred to the action of sun or moon or atmo- 
spheric pressure. 



CHAPTER IX 

ELASTICITY 

Elasticity of Bulk and Form. Rigidity and Incompressibility. Shear and 
Shearing Stress. Extension and Bending. Static and Kinetic Moduli. 
Elastic Constants for Rocks. Milne and Gray. Nagaoka and Kusa- 
kabe. Adams and Coker. Speed of Propagation of Disturbance. 

WE have now to consider the manner in which seismic 
disturbances are transmitted through the material of the 
earth. This, as pointed out in chapter i, depends on the 
elasticity of matter. 

The theory of elasticity is in the main concerned with the 
behaviour under stress of homogeneous isotropic substances ; 
and its application to movements in the intensely hetero- 
geneous crust of our earth might at first seem to be alto- 
gether beside the mark. But the very irregularity of the 
heterogeneity may reasonably enough give to the earth's 
crust properties in the broad, more nearly resembling those 
of the homogeneous solid than of any definable crystalline 
substance. Moreover, the crust is a mere fraction of the 
earth ; and the earth as a whole may respond to elastic 
disturbances in a manner practically identical with the 
behaviour of an ideal sphere isotropic at each point, but 
varying from point to point in its physical and dynamical 
properties. Seismological studies have indeed indicated 
that this conception of the structure of the earth is suffi- 
ciently probable ; but even if it were not so the discussion 
of the elastic properties of such an ideal globe must tend 
to a greater intelligibility of what does occur in the real case. 

Any application of elastic theory to the elucidation of 
earthquake phenomena is necessarily only approximate, 
and must not be supposed to mean that the earth is a homo- 
geneous isotropic elastic solid. This was clearly recognized 
by Hopkins, who was the first to treat earthquake motion 
as illustrative of elastic vibrations. 



IX ELASTICITY 157 

There are two lines of discussion which are important. 
There is first the manner in which rock masses resist and 
yield to the combinations of stress brought to bear upon 
them. This might be called the statics of earthquakes. 
Then there is the transmission of the disturbances so pro- 
duced through the mass ; evidently a kinetic problem. 

When the form or bulk of a substance is in any way 
altered, the strain so produced in the vicinity of any point 
is associated with a definite stress whose components can 
be expressed in terms of the components of strain. The 
simplest case is that of an isotropic body which has been 
changed in bulk only. The associated stress is equal-valued 
all round, being a simple hydrostatic pressure when the 
volume is diminished, and an isotropic tension when there 
is expansion of volume. The ratio of the change of unit 
volume to the increase of pressure producing it is called the 
compressibility of the substance. In the case of liquids 
and solids the compressibility is a small quantity, for it 
requires a considerable stress to produce a measurable 
strain. It is more convenient for present purposes to follow 
Sir George Darwin's example and use the reciprocal of the 
compressibility, namely, the incompressibility, as the elastic 
constant. The larger the incompressibility the more nearly 
does the substance approach the ideal condition of a sub- 
stance absolutely incompressible. For most practical pur- 
poses water may be treated as an incompressible fluid ; 
but when we come to consider the propagation of ' sound 
waves ', that is, waves of compression and dilatation 
through it, we must treat it as a substance with a finite 
though small compressibility. All known substances possess 
compressibility, and therefore all can transmit disturbances 
involving change of volume or change of density. In other 
words, elasticity of bulk is a general property of matter, 
and the incompressibility is the modulus or multiplier by 
which we pass from the given strain (in this case compression) 
to the corresponding stress. 

Fluids possess elasticity of bulk only ; for when any 
change of form is effected in the heart of a mass of fluid 
there is no tendency to recover the original form. It is 



158 



EARTHQUAKE PHENOMENA 



IX 



otherwise, however, with solids, which resist to a greater 
or less degree any effort to change their shape. Extension, 
flexure, and twist are the familiar modes in which solid 
bodies are distorted ; and to these kinds of strain there 
correspond appropriate stresses, whose values can be 
estimated in terms of the strains by multiplication by 
a definite modulus. Now just as there is a strain involving 

pure change of volume 
without change of form, 
so there is a strain in- 
* volving change of form 
unaccompanied by any 
change of bulk. The 
simplest type of such 
a strain is the case of 
a cube transformed by 
a sliding of layer over 
layer into a parallel- 
epiped on the same base 
and of the same height 
as the cube. This is 
indicated in the figure. 
The arrow-headed lines 
represent the stresses, 
which by their action 
on certain faces produce 
and support the strain. 
Such a strain is called 
a simple shear, and the 
corresponding stress a 
shearing stress. A more 
symmetrical represen- 





FIG. 29. 



tation of a simple shear is indicated in the second figure, 
where a parallelepiped not quite cubical is sheared into a 
form which might be regarded as the image of the first form 
in a plane mirror. The figure shows only a section parallel 
to the plane of the shear. There is no change of area ; but 
there is a lengthening along the one diagonal and a corre- 
sponding shortening along the other diagonal. This indeed 



IX ELASTICITY 159 

is another method of representing a shear, and the 
corresponding stress may be described as being composed of 
a pull or tension in the direction of lengthening, and an 
equal push or pressure in a direction at right angles. In 
this case the modulus by which we pass from the shear to the 
associated shearing stress is called the rigidity. The greater 
the rigidity the nearer does the substance approximate to the 
ideal case of an absolutely rigid solid. 

The simple shear is practically realized when a cylindrical 
bar or wire is twisted about its axis of symmetry. Every 
small element originally cubical becomes sheared by an 
amount which is proportional to its distance from the 
axis. 

Every strain, however, which involves different elonga- 
tions in different directions necessarily involves a simple 
shear or change of form ; and it can be shown that the 
most general strain can be built up of components which 
are either pure volume change or pure form change. When 
a bar is pulled out by a tension in one direction, it suffers 
contraction in all directions perpendicular to this direction 
of pull. The net result is a definite change of volume and 
a definite change of figure. Each of these changes is 
resisted by its appropriate elastic stress. But practically 
the important component of the strain is the extension, or 
change in unit length ; and the modulus or multiplier by 
which we pass from this extension to the associated tension 
is known as Young's modulus. It is an elastic modulus of 
the same nature as the incompressibility and rigidity ; but it 
is not a simple modulus. It is determined by an experiment 
in which volume and form both change. In the mathe- 
matical theory of the elasticity of isotropic solids Young's 
modulus is expressed in terms of the incompressibility 
k and the rigidity n by means of the formula 9nk/(3k +n). 
Now Young's modulus can be readily determined by 
experiment ; and the rigidity also is easily measured by 
torsion experiments. Hence the incompressibility which is 
difficult of direct determination may be estimated from 
a knowledge of the other two. 

In the case of simple flexure, as of a bent bow, the layers 



160 EARTHQUAKE PHENOMENA IX 

on the outside of the bend must be lengthened, and those 
on the inside shortened ; and as we pass from the one side 
of the bent bar or rod to the other, the strain passes through 
diminishing stages of elongation to zero and then increases 
through increasing stages of contraction. The associated 
stress is a tension in the elongated filaments and a pressure 
or longitudinal push in the contracted filaments. Thus 
the problem reduces to a particular case of strains involving 
Young's modulus. When a thin plank or rod is made to 
rest with its ends on two supports at the same horizontal 
level it will sag under action of its own weight ; and a certain 
relation will exist between the length, the droop at the 
middle, the dimensions of the rod or plank, and the value 
of Young's modulus. Should the plank be not flexible 
enough to droop appreciably at the middle, it may be 
made to sag sufficiently by means of a load attached to the 
middle point, or by a pressure applied there ; and again 
a certain relation will exist among the quantities already 
mentioned and the applied load or pressure. The experi- 
mental difficulty is to measure with sufficient accuracy the 
droop, which is necessarily a very small quantity. In 
really delicate work it is not possible indeed to measure it 
directly ; and an indirect method based on optical principles 
is usually applied. 

The method here indicated is particularly convenient 
for measuring Young's modulus for rocks. The earliest 
attempts to obtain this and other elastic constants in con- 
nexion with seismological phenomena were made by Milne 
and Gray in Japan in 1881. Much more recently, Professor 
Nagaoka of Tokyo has investigated the elastic constants of 
a great many rocks of various geological ages ; and his work 
has been greatly extended and developed by Kusakabe. 
A further important contribution to the subject has been 
made by Professors F. D. Adams and E. G. Coker, 1 both at 
the time of the research members of the staff of McGill 
University, Montreal. In their method of experiment 

1 An Investigation into the Elastic Constants of Rocks, more especially 
with Reference to Cubic Compressibility. Carnegie Institution, Washington, 
1906. 



IX ELASTICITY 161 

Young's modulus was measured directly for compressing 
stress by means of a delicate instrument designed by Ewing ; 
and the lateral expansion accompanying the longitudinal 
compression was measured by means of a special apparatus 
designed by Coker x and used already by him in his investi- 
gations on the elastic properties of metals. The ratio of 
the lateral elongation to the longitudinal compression under 
longitudinal pressure, or the ratio of the lateral contraction 
to the longitudinal elongation under longitudinal tension, 
is known as Poisson's ratio. In the elastic theory of isotropic 
solids this ratio is equal to (3k - 2n)/ (6k + 2n), where k and n 
are the incompressibility and rigidity respectively. The 
experiment gives Young's modulus and Poisson's ratio, from 
which the incompressibility and rigidity may be at once 
calculated. 

It should be noted that the methods just described for 
measuring the various elastic constants of a solid substance 
assume the ordinary simple theory for an isotropic substance. 
But it is obvious that the vast majority of rocks cannot be 
regarded as even approximately isotropic. This fact must 
be kept in mind when we are applying any of the results to 
the elucidation of seismic phenomena. 

Thus Nagaoka and Kusakabe measure the rigidity directly 
by torsion experiments ; but the value of Young's modulus 
is deduced from flexure experiments by use of a formula 
which is true only for isotropic solids strained within the 
limits of perfect elasticity. On the other hand, Adams and 
Coker measure Young's modulus directly; but the rigidity 
and incompressibility are got at indirectly by calculation 
from Young's modulus and the measured value of Poisson's 
ratio. 

In the specimens of marbles, granites, and basic intru- 
sives experimented on by Adams and Coker, the value of 
Poisson's ratio varies from 0-1977 for a certain specimen 
of granite to 0-29 for Ohio sandstone. This means, in 
accordance with the usual theory, that Young's modulus 
varies from 2-4 to 2-6 times the rigidity and from 1-8 to 1-2 
times the incompressibility. 

1 Proceedings of the Royal Society of Edinburgh, vol. xxv, p. 452, 1904. 

KNOTT M 



162 



EARTHQUAKE PHENOMENA 



IX 



The relation between Young's modulus and the rigidity 
is, according to the isotropic theory, 

E/2n I =Poisson's ratio, 

which shows that E cannot reasonably be less than 2n or 
greater than 3n. For in the former case we should have 
a negative value for Poisson's ratio, that is, a lateral con- 
traction as well as a longitudinal contraction under a longi- 
tudinal compressing stress ; and in the latter case we should 
have the lateral areal expansion greater than the longitudinal 
contraction, so that, under the same kind of compressing 
stress, there would be increase of volume. 

But if we turn to Nagaoka's original list we shall find 
many examples of rocks for which this ratio of Young's 
modulus to the rigidity is 4, 5, 6, or even 7. This simply 
means that the materials are not even approximately 
isotropic. Indeed, nearly all the rocks which are so charac- 
terized are shales, slates, and schists, the aeolotropy of 
which is apparent at a glance. To such rocks accordingly 
the method of measuring Young's modulus by flexure is 
not strictly applicable. What the experiments give is the 
so-called flexural rigidity, which is not a fundamental 
elastic constant. 

The following table shows how many of the rocks investi- 
gated by Nagaoka lie distinctly outside the limits assigned 
above for reasonable values of Poisson's ratio. They are 
grouped also according to geological age. There are three 
columns containing the number of rocks for which the 
ratio E/n is less than 2, between 2 and 3, and greater than 3. 



Geological 
Age 


Number of Specimens 


2n>E 


2n<E<3n 


E>3n 


Total ; 


Archaean 
Palaeozoic 
Mesozoic 
Cainozoic 



3 


8 


4 
14 
3 
31 


2 

16 




6 ! 
33 

8 
45 



It is curious to note the marked difference between the 
Palaeozoic and Cainozoic groups of rocks in regard to the 
characteristic under discussion. In the older rocks we find 



IX 



ELASTICITY 



163 



proportionately greater deviations from the conditions of 
isotropy. 

Nagaoka's results bring out very markedly the fact that 
the average rigidity in the rocks of a given age is greater 
the older the age. This is shown in the following table of 
the range of rigidities and the average rigidity of the sets 
of rocks investigated. The unit is 10 10 C.G.S. units. 



Geological 
Age 


Number of 
Specimens 


Range of 
Rigidities 


Average 
Rigidity 


Archaean 
Palaeozoic 
Mesozoic 
Cainozoic 


6 
33 

8 
45 


j 16 to 31-6 
4-3 to 31 
2-4 to 23-2 
1-0 to 18-5 


22-3 
14-8 
12-7 
6-3 



Clearly the effect of prolonged pressure and the meta- 
morphic action of the internal heat of the earth are such as 
to increase the resistance to distortion of the materials 
forming the earth's crust. There is at the same time 
a slight increase in the average density of the material with 
age, but the change in density is not nearly so marked as 
the change in rigidity. There is thus a distinct tendency 
for the ratio of the rigidity to the density to increase with 
the geological age of the rock, so that an elastic disturbance 
will be propagated with a higher speed through the more 
deeply seated rock. 

The well-marked imperfect elasticity of many of these 
rocks, especially of the sandstones, is a feature which 
seriously interferes with the determination of the rigidity. 
Nagaoka gives an illustration of the gradual way in which 
a block of sandstone yielded to a comparatively small 
twisting stress, so that after the lapse of twenty minutes 
the accompanying strain had increased from its original 
value by nearly 30 per cent, of that value. In such a case 
there is incomplete recovery when the stress is removed ; 
and the difficulty is to get a true measure of the rigidity. 
It has, as Kusakabe expresses it, a doubly indefinite 
character. It depends upon the previous history of the 
material, and especially upon the manner of approach to 
the final stress and connected strain which are the immediate 

M 2 



164 



EARTHQUAKE PHENOMENA 



IX 



object of inquiry. The phenomenon is well known to all 
who have experimented on the elasticity of metals ; but it 
is particularly evident in the case of sandstone rocks (see 
Fig. 1, p. 15). From our present point of view, namely, the 
propagation of elastic disturbances through the material of 
the earth, the rigidity for vanishingly small strains is what 
is wanted. Now all the experiments show that the smaller 
the strain the higher the rigidity for any particular specimen, 
a fact which is in accordance with the theory of viscosity 
now generally accepted. I content myself with giving the 
highest values of the rigidity obtained by Kusakabe in 
different kinds of rocks. Steel, copper, and flint glass are 
added for comparison. 



Age 


Substance 


Density 


Rigidity 


Speed of 
Propagation 


Archaean 
Palaeozoic 


Serpentine 
Quartz-schist 
Pyroxenite 
Granite 
Marble 


2-71 

2-64 

2-9 

2-54 
2-64 


52-2 
28-9 

49" 
16-9 
9-15 


4-4 
3-3 
4-33 
2-58 
1-85 


Tertiary 


Rhyolite 
Sandstone 
Andesite 


2-36 
2-64 
2-63 


3-12 
2-20 
8-09 


1-16 
1-09 
1-75 




Steel 
Copper 
Flint Glass 


7-85 
8-84 
2-94 


82 
45 
24 


3-23 
2-26 
2-86 



The gradual yielding of the substance to a steady moderate 
stress is not so marked in flexure experiments as in torsion 
experiments. This is to be expected inasmuch as, under 
flexure, part of the rod is in compression, and once the 
limits of practically perfect elasticity are exceeded the 
material will yield more readily to an extending force than 
to a compressing force. From this point of view also 
Adams and Coker's method of experimenting with com- 
pressing stresses is preferable to the more usual and some- 
what simpler method of applying extending loads. 

Adams and Coker selected their rocks with great care, 
having regard to uniform and approximately isotropie 
structure as well as to freedom from all flaws and cracks in 
the test pieces. 



IX 



ELASTICITY 



165 



I reproduce the results in full, with the added information 
of the geological ages and the densities of the rocks used. 1 



Kock 


Age 


Young's 
Modulus 


Polygon's 

Ratio 


Rigidity 


Incoui- 

|nv>-i- 
bility 


Dm- 
ttj 


Black Belgian Marble . 


Palae. 


76-4 


0-2780 


29-82 


57-26 


2-7 


Carrara marble . 


Meso. 


55-4 


2744 


21-71 


40-90 


2-72 


Vermont marble 


Pake. 


52-4 


2630 


20-69 


36-80 


2-71 


Tennessee marble 


Palae. 


62-1 


2513 


24-82 


41-15 


2-70 


i Montreal Limestone . 


Palae. 


63-5 


2522 


25-04 


42-50 


2-69 


; Baveno granite . 




47-1 


2528 


18-75 


31-79 


2-61 


Peterhead granite 


Palae. 


57-1 


2112 


23-40 


33-00 


2-63 


Lily Lake granite 


Palae. 


56-3 


1-1982 


23-30 


31-03 


2-63 


Westerly granite 


Palae. 


50-9 


2195 


20-80 


30-29 


2-63 


Quincy granite ( 1 ) 


Palae. 


46-4 


2152 


19-16 


27-50 




(2) . 




56-8 


1977 


23-73 


31-40 




Stanstead granite 


Palae. 


39-2 


2585 


15-56 


27-18 


2-68 


Nepheline syenite 


Palae. 


62-9 


2560 


25-05 


42-90 


2-62 


New Glasgow anorthosite 


Arch. 


82-5 


2620 


32-75 


57-60 


2-72 


Mount Johnson essexite 


Palae. 


67-1 


2583 


26-70 


46-50 


2-82 


New Glasgow gabbro . 


Arch. 


108-0 


2192 


43-80 


65-89 




Sudbury diabase 


Arch. 


94-9 


2840 


37-00 


73-29 


3 


Ohio Sandstone . . 


Palae. 


15-8 


2900 


6-12 


12-50 





From these values we can calculate the speeds of propaga- 
tion of the various types of wave according to the formula 
given below. The New Glasgow gabbro (density 3, assumed) 
gives the highest distortional speed, namely, 3-8 km. per sec. ; 
and the compressional dilatational speed is 6-4 km. per sec. 
The latter type of disturbance travels slightly faster in the 
Sudbury diabase. Here also there is a tendency for the 
elastic constants to increase with the age of the rock. 

In all these cases it is the static modulus which is being 
measured ; but in the propagation of elastic disturbances 
through the material it is the kinetic modulus which comes 
into play. In the case of metal wires, the kinetic and 
static values of a particular modulus differ slightly ; and, 
according to Kusakabe's ingenious experiments, the difference 
between the kinetic and static values of the flexural rigidity 
in rocks is in many cases of considerable magnitude. His 
method was to measure the period of natural vibration of 
a short rod or prism of the rock, the one end of which was 

1 Dr. Home of the Geological Survey of Scotland furnished me with the 
geological ages of the rocks ; and these were checked by Professor Adams 
when he supplied me with the densities. 



166 EARTHQUAKE PHENOMENA IX 

firmly clamped. The free end was kept in vibration like 
a tuning fork by taps of a hammer worked by an electro- 
magnet. To this free end was attached a fine copper wire, 
which was led over a bridge and kept in a state of suitable 
tension by an appended weight. The vibrating prism of 
rock imposed a forced vibration upon the wire, the length of 
which was carefully adjusted until the amplitude of vibration 
attained a maximum. This happened when the vibration 
period of the rock prism was one of the natural periods 
of vibration of the stretched copper wire. Since this could 
be calculated in terms of the length and tension of the wire, 
the period of vibration of the rock became known ; and 
application of the usual theory gave the flexural rigidity and 
the kinetic Young's modulus. Bearing in mind the im- 
perfect elasticity of rock as evidenced by the yielding during 
application of stress, we should expect the static modulus 
to be less than the kinetic modulus, since in the latter case 
the strains are smaller and there is no opportunity for the 
time lag to declare itself. This was what Kusakabe found to 
be generally the case ; but there were a good many instances 
in which the kinetic modulus was the smaller. This i& 
probably to be referred to the different condition of the 
material in the two experiments. Kusakabe himself showed 
that the presence of moisture in the specimen had a great 
effect upon the value of the flexural rigidity, making the 
material much less resistant than in the dry state. As 
pointed out by Nagaoka, this suggests that superficial 
earthquakes may be more likely to follow times of heavy 
rains, which, by soaking through the rocky crust, will 
render it more liable to yield to stresses acting on it. It is 
interesting to note in this connexion that the inhabitants 
of Comrie in Perthshire, some fifty years ago when shocks 
were frequent in that locality, believed that earthquakes 
were more frequent after than before excessive rainfall. 

Some of the most important applications to be made have 
to do with the propagation of elastic disturbances through 
the material of the earth. The speed of propagation of 
a disturbance through an elastic substance depends upon 
the density of the substance and the appropriate elastic 



IX ELASTICITY 167 

modulus. In every case the square of the speed of propaga- 
tion is measured by the ratio of the modulus to the density, or 

V 2 =E/D 



where E represents the modulus and D the density or 
mass in unit volume. 

In the case of fluids there is only one kind of elastic modu- 
lus, namely, the incompressibility ; and the elastic disturb- 
ance must be a change of density with a corresponding 
change of pressure. The most familiar example is the 
transmission of sound through air, by means of a succession 
of condensations and rarefactions. This condensational 
rarefactional disturbance is audible as sound, because the 
pressure and density vary at a sufficiently rapid rate. 
Condensations and rarefactions may follow one another at 
too slow a rate to be recognizable as sound ; but the air is 
none the less transmitting elastic vibrations, although our 
sense of hearing is unable to detect them. Not until the 
successive maxima and minima of pressure follow one 
another at a rate of thirty or forty times a second does the 
passing disturbance appeal to our sense of hearing. The 
bearing of this on earthquake sounds has been discussed in 
chapter ii. 

When the successive disturbances follow one another at 
regular intervals we speak of them as forming a train of 
waves of a definite period and wave-length. The period is 
the time taken by any small portion of the medium to go 
through all its phases of configuration and come back to the 
original state of pressure and volume. During the lapse of 
time equal to one period the disturbance advances a wave- 
length. Hence the speed of propagation is equal to the 
wave-length divided by the associated periodic time. In 
rapid vibratory motion this periodic time is so short that 
it is often more convenient to speak of the number of vibra- 
tions or pulses per second. This number is called the 
frequency ; its value is numerically equal to the reciprocal 
of the periodic time. Hence we find that the speed of 
propagation is equal to the product of the wave-length 
and the frequency, a relation which enables us to calcu- 



168 EARTHQUAKE PHENOMENA IX 

late the wave-length when the other two quantities are 
known. 

When we pass to the consideration of elastic solids we 
see that different kinds of elastic disturbances may be 
propagated corresponding to the different kinds of elasticity 
involved. Imagine, for example, a long straight wire with 
the one end fixed, and let a twist be given to the free end. 
This twist will travel to and fro along the wire with a speed 
which is measured by the square root of the ratio of the 
kinetic rigidity to the density. Again, if a blow be struck 
on the end in the direction of the rod or wire, a longitudinal 
disturbance will be started which will run to and fro along 
the rod with a speed equal to the square root of the ratio of 
the kinetic Young's modulus to the density. A wooden 
rod, tightly clamped at the lower end, may be made to 
emit a musical note of a definite pitch by gently drawing 
over its surface with a steady pressure a piece of resined 
leather. The friction sets up longitudinal vibrations which 
pass to and fro along the rod like the air pulse along a closed 
organ pipe. 

The speed of propagation of elastic disturbances through 
extended masses does not, however, depend on Young's 
modulus either directly or indirectly. The speed of propa- 
gation of what is known as the condensational wave depends 
upon a modulus which is equal to the sum of the incom- 
pressibility and ^ of the rigidity in symbols, k +4^/3. 
Within the limits assigned above for the value of Young's 
modulus relatively to the rigidity, this wave modulus is 
always greater than Young's modulus. It is also obviously 
greater than the rigidity. Hence the so-called condensa- 
tional wave in elastic solids is propagated with the greatest 
speed of all the possible waves which have been referred to. 
It is well to note that this disturbance of most rapid trans- 
mission involves change of shape as well as change of volume, 
so that both the fundamental moduli enter into the ex- 
pression. 

In addition to this condensational disturbance, there may 
be a purely distortional disturbance propagated through 
the extended mass with a speed which depends only on the 



IX ELASTICITY 169 

rigidity. The displacements of the medium which accom- 
pany the passing of this type of wave take place at right 
angles to the direction in which the wave is being propagated. 
It is often referred to as the transverse wave, because of 
the vibratory motions being transverse to the direction of 
propagation, just as in the case of a tightly stretched string. 
Similarly the wave of mixed modulus, k + 4w/3, is sometimes 
spoken of as the longitudinal wave. 

The surface undulations which are experienced near the 
epicentre of a strong earthquake imply flexural strains in 
the surface layers, and the speed of propagation of these 
waves may depend partly on the flexural rigidity and partly 
on gravity. They can hardly be considered as purely 
elastic, and are no doubt powerfully influenced by the 
viscosity of the material. Away from the immediate region 
of the earthquake origin, and well below the surface, the 
vibrations which are transmitted are certainly not flexural ; 
and under the necessary constraints at great depths they 
are less influenced by viscosity. 



CHAPTER X 

ELASTIC WAVES 

Reflexion and Refraction of Waves. Two Flexible Ropes of Different 
Weight. Two Elastic Media with a Common Boundary. One type 
of Wave Motion in Fluids, Condensational. Two Types of Wave 
Motion in Solids, Condensational and Distortional. Reflexion and 
Refraction of Elastic Waves and Boundary of two Media. Rock and 
Water. Rock and Rock. Rock and Air. Water and Air. Earth- 
quake Barriers. Seismic Energy largely retained in Crust. Inter- 
ference Phenomena. Viscosity. Wave Groups. 

LET us imagine a disturbance of a complex character 
originating some ten or twenty miles below the earth's 
surface. This will generate in the surrounding material 
two distinct types of wave motion propagated with different 
velocities. Each type will suffer reflexions and refractions 
at surfaces separating regions of different physical proper- 
ties ; and will also experience reflexion wherever it impinges 
internally on the surface of the earth. The final result will 
be an excessively complex motion at every point of the 
shaken area. 

The dynamical process by which waves are propagated 
and by which they pass from one medium to another for 
the process is one and the same may be illustrated by 
experiments with ropes or flexible cords not too tightly 
stretched. 

For example, fix the one end of an ordinary clothes' rope 
to a point eight feet or more above the floor, and hold the 
other end in the hand so that the rope hangs freely in air. 
If now the rope be drawn down by the other hand and then 
let go a disturbance will be observed passing along the rope 
to the point of fixture in the wall, and then back again 
after reflexion. The hand which holds the rope will feel 
a succession of tugs as the disturbance comes back after 
successive reflexions at the far end. 

The essential phenomena are studied to greater advantage 



X ELASTIC WAVES 171 

by use of a flexible cord heavier than the ordinary rope. 
This is conveniently done by filling a long piece of rubber 
tubing with small shot. With such an arrangement the 
disturbance passes along at a comparatively slow rate, and 
the instants of its reflexion at the two ends can be timed 
with ease. Let a second piece of tubing of narrower bore 
be similarly filled. Then, when the two are set side by 
side and simultaneous disturbances are sent along them 
it will be seen that the disturbance travels more quickly 
along the thinner tube, that is, the tube weighing less per 
foot. Now let the two tubes be tied together, end to end, 
at (7, so as to form a single stretch, the other extremity 
B of the heavier tube being fixed to the wall, while the free 
extremity A of the lighter tube is held in the hand. By 
plucking the tube near A we start a disturbance which 




travels along towards C with the speed belonging to the 
thinner tube. On reaching C the disturbance separates into 
two parts, the one part passing back by reflexion towards 
A, and the other part passing on with a slower velocity of 
propagation towards B. Here it is reflected and passes 
back towards (7, where again it breaks up into two parts, 
one of which continues towards A, while the other is re- 
flected towards B. Meanwhile the first reflected part in 
the thinner tube suffers reflexion at the hand, and is sent 
towards C again, once more to be split up into two. 

Now if instead of a ' point boundary ' between two 
flexible strings of different weight and tension, we think 
of a ' surface boundary ' between two extended masses of 
different density and elasticity, we pass to the case of the 
propagation of elastic waves through solids. Let us sup- 
pose for simplicity that the interface between the two elastic 
media is a plane, and that the disturbance travelling in the 



172 EARTHQUAKE PHENOMENA X 

one medium is of such a nature that it actuates every point 
of the interface with exactly the same kind of motion at 
the same instant. Such a disturbance is called a plane 
wave with its wave front parallel and its direction of propa- 
gation perpendicular to the interface. This wave is falling 
normally on the interface ; and the wave started in the 
other medium will pass on with different speed, but still 
in the same direction as the original wave of disturbance. 
At the same time, just as in the case of the two flexible 
tubes, a ' reflected ' wave will be sent back into the first 
medium. 

When, however, the disturbance falls obliquely on the 
interface so that different parts of the interface are affected 
at different times, the problem becomes much more com- 
plicated. The plane wave sweeps along the interface in 
a manner similar to the way in which a long roller is often 
seen to sweep along the side of a breakwater, each part of 
the breakwater receiving the dash of the wave at a different 
instant of time. From each successively disturbed point 
of the interface disturbances are passed on into the second 
medium and also back into the first medium ; and these 
disturbances will combine to form resultant plane waves 
propagated in the respective media. The manner in which 
a series of disturbances combine to form well-marked wave 
fronts may be illustrated by dropping into a stretch of still 
water a metal rod inclined to the horizontal. The disturb- 
ance begins where the lower end of the rod first touches the 
water ; and when the whole rod has become immersed, 
the disturbed region of the water will be seen to be 
bounded by two wavelets forming a wedge, which gradu- 
ally increases in size as the wavelets pass outwards in each 
direction. 

When the two media are elastic solids a special com- 
plexity comes in because of the two types of waves referred 
to in last chapter. Even if the original disturbance in the 
first medium be of one type only it will, except under very 
special conditions, generate at every boundary where 
reflexion and refraction occur not only reflected and refracted 
waves of its own type, but also those of the other type. 



X ELASTIC WAVES 173 

This is at once seen to be necessary when we picture to 
ourselves the nature of the motion accompanying the 
transmission of the two types of wave. When the plane wave 
is of the distortional type the vibrations of the particles 
of the medium take place in the wave front, that is, per- 
pendicular to the direction of propagation of the wave. 
In the condensational type of wave the vibration of the 
medium has a component perpendicular to the wave front, 
and in the case of plane waves passing through an extended 
solid the vibration is wholly in this direction normal to the 
wave front, that is, parallel to the direction of propagation 
of the wave. 

In the case of oblique incidence, the longitudinal vibration 
in the incident wave will produce a disturbance in the 
boundary which cannot possibly be normal to the wave 
front of the reflected wave. There will be a component in 
the wave front of this reflected wave, and consequently 
a distortional transverse wave will be started with a trans- 
verse vibration. Hence, in general, an obliquely incident 
dilatational wave will give rise to a distortional as well 
as a dilatational reflected wave in the first medium, and 
also two refracted waves, one distortional and the other 
dilatational, in the second medium. Similarly a purely 
distortional wave incident obliquely on the boundary will 
generate four waves altogether, two refracted and two 
reflected. 

The various angles of reflexion and refraction are easily 
calculated in terms of the angle of incidence, it being noted 
that the surface trace is common to all the waves. The 
speed of propagation of each wave is, so to speak, the com- 
ponent in its direction of the speed of propagation of the 
surface trace. 

For example, 1 let a condensational wave be incident at 
an angle 6 to the boundary surface separating two media ; 

1 The results which follow, as well as much of what precedes, are taken 
from my paper on the Reflexion and Refraction of Elastic Waves with 
Seismological Applications (Phil. Mag. for July 1899), which paper was 
a reprint with additions of a previous elastic discussion ot Eartkquak - 
and Earthquake Sounds (Trans. Seism. Soc. of Japan, vol. xii, 1888). 



174 EARTHQUAKE PHENOMENA X 

and let v, v' be the speeds of propagation of the condensa- 
tional waves in these two media, and u, u' the speeds of 
propagation of the distortional waves. The corresponding 
angle 0' for the refracted condensational wave, and the 
angles 0, <j>' for the reflected and refracted distortional 
waves, are given by the equations 

v/sin 6 = v'/sin 6' = it/sin = u'/sin $'. 

Now, as u is less than v, there will always be a reflected 
distortional wave, except at normal incidence when 6 = 0, 
and at grazing incidence when = 90. There will be 
refracted waves for all except the limiting incidences, if v is 
greater than v'. If v should be intermediate in value to v 
and u', there will be no refracted condensational wave for 
angles of incidence higher than a certain critical angle ; 
the condensational wave will be totally reflected. If v 
should be less than both v' and u', there will be special angles 
of total reflexion for both kinds of waves. When the critical 
value corresponding to the refracted distortional wave is 
reached there will be total reflexion of both types of wave, 
and the whole energy of the incident wave will be divided 
between the two reflected waves. 

If the incident wave is a distortional wave, there must 
always be a critical angle of incidence for and above which 
the reflected condensational wave vanishes. The existence 
of such critical angles for the refracted waves will depend 
upon the relative values of u, v', u' the condition for 
the possibility of total reflexion being that v is less 
than v f . 

If one of the media is a fluid, there can be no distortional 
wave in it. This therefore forms a distinctly simpler case 
than when the media are both elastic solids, and a somewhat 
detailed account of a special case will be of service in indi- 
cating the manner in which a wave breaks up at the boundary 
of two substances. 

Let us take water and rock 1 as the two media, the 

1 The elastic constants here used were selected in 1888 on the basis of 
Gray and Milne's experiments. A comparison with the table on page 165 
shows that they represent an inferior type of granite. 



X 



ELASTIC WAVES 



176 



constants being assumed to be as in the following 
table : 





Water 


Rock 


Density . 


1 


3 


Incompressibility. . . 
Rigidity 


2-2 xlO 10 


25 x 10 10 
15 x 10 1C 


Speed of v wave . . . 
Speed of u wave . . . 


0-883 


2-39 
1-38 



The following tabulated results have been worked out for 
the case of a disturbance passing from rock to water. The 
quantities tabulated are the energies in the various types 
of wave, that of the incident wave being taken as unity. 
In the first table the incident wave in the rock is condensa- 
tional ; and since this kind of wave in the rock has a higher 
speed of propagation than either of the other two, there are 
no critical angles of total reflexion. In the second table 
the incident wave is distortional ; and as its speed of propa- 
gation is less than that of the condensational wave in the 
rock, there is a critical angle of incidence for and above which 
there is no reflected condensational wave. 

The quantities A, A^ A' represent the energies of the 
incident, reflected, and refracted condensational waves ; 
B, J5j, B' the energies of the similar set of distortional waves. 
The corresponding angles of incidence, reflexion, and refrac- 
tion are given in contiguous columns referring to the 
condensational and (/> to the distortional waves. 

INCIDENT WAVE CONDENSATIONAL 



Incident 


Reflected 


Refracted 


Reflected 


6 


A 


A, 


S 


A' 


0i 


B, 







599 





401 








10 




536 3 49' 


397 


5 45' 


071 


20 




377 7 32' 


370 


11 23' 


254 


30 




195 


11 2' 


333 


16 35' 


456 


40 




056 


14 15' 


293 


21 47' 


660 


50 


006 


17 4' 


244 


26 15' 


753 


60 


014 


19 22' 


206 


30 


775 


70 


031 21 5' 


188 


32 15' 


783 


80 


000 22 9' 


182 


34 39' 


818 


89 


616 22 31' 


069 


35 16' 


314 


90 


1 








EARTHQUAKE PHENOMENA 

INCIDENT WAVE DISTORTIONAL 



Incident 


Reflected 


Reflected 


Refracted 


e 


B 


B, 


*, 


A, 


B' A' 





1 


1 





000 


-000 


10 23' 


1 


711 


20 


253 


7 32' -036 


21 47' 




222 


40 


656 


14 15' -126 


30 




014 


60 


779 


19 22' -206 


34 39' 




027 


80 


815 


22 9' -157 


35 16' 




679 


89 


311 


22 31' -007 


! 35 6' 




1 


90 


000 


22 31' -000 


36 




584 




22 56' -415 


! 40 




461 




25 14' -539 


50 




504 




30 33' -495 


60 
; 70 




-506 
520 


Non-existent 


35 4' -494 
38 34' -480 


, 80 




634 




40 47' -366 


, 89 45' 




818 




41 34' -183 


! 90 




1 




000 



In the first table B and B' of course do not appear, and 
in the second table A and B' do not appear. 

It should be mentioned that each wave-energy is calcu- 
lated independently ; and a test of the accuracy of the 
calculations is afforded by the condition that the energy 
of the incident wave must be fully accounted for. In other 
words, since in every case the incident energy (either A or B) 
is taken as unity, the sum of all the others must be unity. 

The chief peculiarities embodied in these tables are shown 
graphically in the corresponding curves (Fig. 31). Any 
one curve represents the manner in which the energy of 
each wave depends on the angle of incidence. The angles 
of incidence are measured off along the horizontal line ; 
and the corresponding energies are represented by the 
ordinates perpendicular thereto. The energy of the incident 
wave is represented by the straight line at unit distance 
from the line along which the angles of incidence are 
measured off, i. e. the top horizontal line. 

The first set of curves shows the state of things for an 
incident condensational wave. For the sake of brevity, we 
shall occasionally refer to the different waves by the letters 
A, A lt A', J5, B 19 chosen to represent their energies. At per- 
pendicular incidence condensational waves only are started at 
the bounding surface ; and as the angle of incidence increases 



ELASTIC WAVES 



177 



the energies of both of these diminish. A', -the energy of 
the wave in the water, seems to fall off continuously until 
it vanishes at grazing incidence. The ,4-wave, however, 
vanishes at two distinct incidences, and after 80 is reached 
begins to increase till at 90 it attains unity. The behaviour 
of this reflected condensational wave is extremely curious, 
the wave being practically non-existent for incidences 
between 50 and 80. The greater part of the energy of 
the incident wave is then accounted for by the B l or reflected 

ROCK AND WATER INTERFACE 

A B_ B 




7 



0* 20 . 4-0* 60* 60* 0* "0* 40 60* 80" 

Condensational Wave incident Distortional Wave incident 
FIG. 31. 

distortional wave. For incidences higher than 45 three- 
quarters of the whole incident energy is so transformed. 
It will be noticed that up to pretty high angles of incidence 
the energy transmitted to the water does not suffer any very 
great falling off. 

Turning now to the second set of curves, which show the 
state of things for an incident distortional wave, we meet 
with some very curious relations. For reasons already 
discussed, the A r wave cannot exist for incidences higher 
than a certain critical value, which depends on the rock 
itself. The energy of this wave, however, attains a con- 
siderable maximum value for an angle of incidence slightly 
below this critical value. Almost for the same incidence, 
the energy of the jB r wave falls to a very low minimum, 

KXOTT N 



178 EARTHQUAKE PHENOMENA X 

almost vanishing indeed. Comparing this first portion of 
the second set of curves with the first set of curves as a whole, 
we see a general resemblance between the two. That is, 
the energy of the reflected wave of the same type as the 
incident wave rapidly falls off to a minimum as the angle 
of incidence grows, while that of the reflected wave of the 
other type rapidly increases to a maximum. Finally the 
energy of the reflected wave of the same type, in both cases 
quite abruptly, runs up to equality with the incident wave. 
In the second set of curves this happens at the angle of 
total reflexion ; for, not only does the A r wave vanish, but so 
also does the A '-wave which indeed never attains any great 
significance at the lower incidences. After the critical angle 
of incidence is passed, however, the energy of the .4 '-wave 
soon reaches a maximum, being then of greater value than 
that of the I^-wave, and gradually falls away to zero, while 
the energy of the ^-wave as gradually rises to unity. 

A glance at the two sets of curves shows that the inci- 
dent distortional wave is, at the higher incidences, much 
more efficient than the condensational wave in creating a pro- 
gressive disturbance in the water. The angle of refraction 
can never exceed 42 ; so that even for very high incidences 
the wave in the water will travel upwards to the surface 
fairly directly. Here I think we may have the explana- 
tion of the curious bumpings which have sometimes been felt 
at sea (chapter vi). Sounds will be heard if the periodic 
time of any of the components in the wave-motion is short 
enough, and if at the same time the intensity is sufficient 
to give rise to audible sound waves in the air, either directly 
or indirectly through the medium of such a solid as a ship. 
According to Colladon's experiments at the Lake of Geneva, 
the speed of sound in water at 8-lC. is 1435 metres per 
second. This gives 14-35 metres (or about 8 fathoms) for 
the wave-length of a wave whose pitch is 100 vibrations 
per second. A slower vibration will of course give a longer 
wave-length ; and a quicker a shorter. But enough has been 
said to show that in such a wave of condensation we have 
something quite fitted to affect even a large ship as a whole. 

All that has been said regarding the transference of 



ELASTIC WAVES 



179 



vibrations from rock to water will, in a general way, hold 
true of their transference from rock to ah*. The point of 
special interest is that whatever be the angle of incidence 
in the rock the refracted wave will pass into the air in 
a direction which is very slightly inclined to the normal. 
Thus the incompressibility of air being 1-41 x 10 6 , and the 
density 0-0013, we find for the speed of propagation the 
value 0-329 kilometres per second, or 0-204 miles per second. 
With the same values as formerly for the rock constants 

sin 0' = 0-085 sin 6 = 0-147 sin (f>. 

If 6 = 90, 6' will be 4 54', so that with the condensational 
wave incident in rock at nearly grazing incidence the re- 
fracted condensational wave in air will pass off in a direction 
only 5 removed from the direction of the normal. Simi- 
larly for the distortional wave in rock incident at grazing 
incidence (0=90) the resulting refracted condensational 
wave in air will make an angle of only 8 30' with the 
normal to the surface. At whatever incidences the various 
disturbances in the rock impinge upon the surface, the 
disturbance transmitted into the air will pass off in direc- 
tions which will all be included within a small cone with axis 
along the normal and of semi-vertical angle less than 9. 

The following detailed calculation is made for the case of 
a rock whose elastic constants are as above, but whose 
density is 2000 times that of air. The speeds of propaga- 
tion will be less than the former values in the ratio of 0-931 
to 1. 

DISTORTIONAL WAVE INCIDENT IN ROCK 



Incident 


Reflected 


Refracted 


</ 


i^ 


BI 


B 


A, 


6' 


A' 


1 


1 












14 2' 


534 25 


466 


l-6 


00002 


26 34' 




025 


51 


975 


3 


00006 


33 40' 




003 


74 -997 


3-7 


00006 


35 13' 




1 


90 


3-8 





39 48' 




1 imaginary 


4-3 


00019 


45 




1 


4-7 -00016 


59 2' 


1 


1 


5-7 -00014 


73 18' 1 


1 


6-3 -00014 


84 17' 1 


1 ., r, i, -00006 



N 1' 



180 



EARTHQUAKE PHENOMENA 



CONDENSATIONAL WAVE INCIDENT IN ROCK 



Incident 


Reflected 


Refracted 


$ 


A 


A, 


e f 


-v, 







1 




00013 


14 2' 




828 


0-9 


00013 


26 34' 




464 


l-7 


00011 


45 




079 


2-7 


00009 


59 2' 




0002 


3-3 


00007 


73 18' 




003 


3-7 


00006 


84 17' 




091 


3-8 


00005 



Reflected 



o 



8 
15 
24 
30 
34 
35 



B, 

17-2 

536 

921 

9997 

997 

909 



The energy which escapes into the air is so small that 
practically the whole energy remains in the rock. The 
general behaviour of the phenomenon is very similar to 
what was found in the case of rock and water, the differences 
being differences of degree and not of kind. Thus we may 
make the graphs for rocks and water serve in a rough way 
for rock and air by imagining a few slight changes to be 
made. In the graph for the incident condensational wave, 
imagine the distortional-energy curve, B v to run up into 
practical contact with A when the angle of incidence is 
about 60, to remain very near to it till about 75, and then 
to fall rapidly away to zero at 90. At the same time, 
because of the great minuteness of the refracted energy, 
A', the reflected condensational energy A t begins, at zero 
incidence, with practically unit value, and is to a very close 
approximation the inversion of B v In like manner, the 
incident distortional wave is, for incidences between and 
the critical angle 35 13', practically represented by the 
two reflected waves. The reflected distortional energy 
begins and ends with value unity, passing through a small 
minimum value immediately before the critical angle is 
reached ; while the reflected condensational energy begins 
and ends with zero and passes through a corresponding 
maximum which is practically unity. The refracted 
condensational energy, A', is very small throughout, and 
could not be shown graphically with the others unless it 
were drawn to a scale of at least 1000 to 1. Immediately 
after the critical angle is past the condensational energy in 



X 



ELASTIC WAVES 



181 



the air rises abruptly to the greatest value it ever attains, 
about l/5000th of the whole, and faUs off steadily with 
increasing incidences until it vanishes at grazing incidence. 
Practically the whole energy is retained in the solid in the 
purely distortional form. 

The following example of the behaviour of waves at the 
plane surface of rock and fluid, whose density and com- 
pressibility are equal to those of the rock, may claim some 
attention as a case which may arise when lava or molten 
rock is in contact with solid material. 

DISTORTIONAL WAVE INCIDENT IN THE ROCK 



Incident 


Reflected Refracted 


* 


B 


B L 6 


A! & 


\' 







1 










14 2' 




725 25 


144 


18 


131 


26 34' 




318 


51 


261 


35 


421 


35 13' 




1 


90 





48 





45 




147 


imaginary 66 


853 


50 44' 




1 


90 





Higher in- ) 
cidences ] 


1 


1 


99 


imaginary 



CONDENSATIONAL-RAREFACTIONAL WAVE INCIDENT IN THE ROCK 



Incident 


Reflected 


Refr 


acted 


Reflected 


e A 


A, 


& 


A' 


B, 





021 





979 





14 2' 


007 


10 


937 


8 -055 


26 34' 


003 


19 


839 


15 -158 


45 


104 


32 


646 


24 -256 


59 2' 


240 


40 


503 


30 -256 


73 18' 


268 


46 


471 


34 -261 


84 17' 


039 


48 


618 


35 -344 


90 1 


1 


48-2 





35-3 



The chief peculiarity in the first of these cases is, perhaps, 
the vanishing at two incidences of the refracted wave in the 
fluid. It vanishes at the critical angle (35 13') at which 
the reflected condensational wave disappears ; and then it 
has its own critical angle (50 44'). 

Between these limits its energy rises to a pronounced 



182 



EARTHQUAKE PHENOMENA 



maximum. In these respects there is a broad similarity 
between this case and the cases of rock and water, and rock 
and air. The differences are only differences of degree, 
depending on the different relations among the densi- 
ties. 

Some of the results given may be more easily understood 
if presented in the following way. 1 





FIG. 32. 

Each figure shows approximately the manner in which 
the energy of a particular type of wave at a particular angle 
of incidence is distributed among its derivatives of both 
types. The incident ray is represented by the broadest 
line passing downwards from left to right. The upper 
medium is rock, and the lower water. Since condensational 
waves only can exist in a fluid, there is never more than 

1 Taken from an abstract of an Address published in the Proc. Roy. 
Soc. of Edin., vol. xxii, 1899. 



X ELASTIC WAVES 183 

one ray in the lower medium. In all the figures, C represents 
a condensational-rarefactional wave, and D a distortional. 
The first two figures show how an incident condensational 
wave breaks up into two reflected waves and one refracted 
wave. The angles of incidence are 36 and 80 respectively. 
In both cases the greater part of the energy is reflected in 
the distortional form, and in the second case the reflected 
condensational wave is practically non-existent. The num- 
bers attached to the different rays indicate roughly the 
amounts of energy associated with them. 

In the four remaining figures the behaviour of an incident 
distortional wave at various incidences is shown. The con- 
densational wave travels faster than the distortionai wave, 
and is therefore in all cases reflected at a greater angle. 
When the angle of incidence approaches 35 (see fourth 
diagram), the reflected condensational wave is sent off at 
a very high angle, and carries away with it most of the 
energy, about 80 per cent., while the amount of energy 
associated with the reflected distortional wave is excessively 
small. At a slightly greater angle of incidence, namely, 
35 16', the reflected condensational wave passes off parallel 
to the surface with zero energy, and at higher incidences 
has no existence. With the vanishing of the reflected 
condensational wave at this critical angle, the refracted 
condensational wave also vanishes a very remarkable 
result. Consequently at this angle all the energy is reflected 
back into the rock in the distortional form. See the fifth 
diagram, showing by a dotted line the direction which the 
refracted ray would have had if it had existed. For higher 
incidences the refracted ray comes strongly into evidence, 
accounting for approximately half the energy, but becoming 
less important at very high incidences, until at grazing 
incidence nothing is left but the reflected distortional wave. 

In the paper in the Philosophical Magazine detailed calcu- 
lations will be found for the more complex cases in which 
both the media are elastic solids through which the elastic 
waves are propagated with different speeds. The general 
nature of the results are, however, sufficiently indicated by 
the examples already given. 



184 EARTHQUAKE PHENOMENA X 

The main point is that when we have to do with transi- 
tions from one medium to another the character of the 
wave-motion may alter fundamentally. A comparatively 
simple type of vibration will speedily become transformed 
into a complicated combination of types. When we con- 
sider the heterogeneous nature of the crust of our earth we 
can have no difficulty in understanding the great complexity 
of earthquake movements. Even although the disturbance 
may for the greater part of its course have passed through 
fairly homogeneous material it cannot reach us except 
through the excessively heterogeneous structure familiar to 
the geologist. In this last stage of its progress it must 
become greatly altered from what it was originally. 

If, again, different types of seismic motion can be dis- 
tinguished at the surface of our globe, we seem compelled 
to assume that their separability depends upon their having 
traversed long stretches of fairly homogeneous material. 
It is easy to see that under such conditions the compressional 
waves in this approximately homogeneous portion would 
outstrip the distortional waves ; and this separation in 
time of the first appearance of each type would be apparent 
at the surface, although the motions might not otherwise be 
distinguishable the one from the other. We shall return to 
this in the next chapter. 

Another important point touched on in the above investi- 
gation is the possibility of barriers to the propagation of 
seismic disturbances. Any large dislocation or fault may 
stifle the movements, while the existence of total reflexion 
may greatly modify the transmission across a boundary 
when the manner of incidence is but slightly altered. 

The earth's surface is itself a most effective barrier, a 
very small fraction indeed of the original energy being 
transmitted to the air. Thus, at whatever angle elastic 
disturbances may impinge internally upon the earth's surface, 
by far the greater part of the energy is reflected within the 
crust and is transmitted through it by a succession of in- 
ternal reflexions until the energy of motion is frittered away 
as heat in virtue of the viscosity of the rock. 

In the cases detailed above marked complications arise 



X ELASTIC WAVES 185 

in virtue of the (comparatively simple) theory of perfect 
elasticity. In real cases of transmission of earthquake dis- 
turbances we have to deal with motions which are only quasi- 
elastic. For the treatment of such kinds of motion our 
mathematical methods are not powerful enough. But we 
may be sure that these quasi-elastic disturbances will be 
accompanied by even more complicated changes than those 
indicated above. 

The complexities of wave-motion are indeed quite beyond 
our powers of analysis. Once the displacements become 
greater than the limits within which a simple elastic theory 
is applicable we really do not know what may happen. 
To a first approximation the speeds of propagations are 
assumed to depend only on the elastic constants and the 
densities. Waves then become simply superposable. But 
in many, indeed in most, cases this simple superposability 
does not hold. Interference phenomena of a complicated 
nature are frequently present. Again the viscosity of the 
material must seriously affect the transmission of disturb- 
ances through it ; and this viscosity will be more effective 
in the broken stratified and faulted crust than in the layers 
deeper down. The quicker vibrations will be killed out 
more rapidly than the slower vibrations. Different types 
of vibrations will coalesce to form wave groups whose 
apparent speed of propagation may not be the real speed of 
propagation of any single type of wave. Some of these 
more difficult questions have been considered by Nagaoka, 
who has attempted in this way to explain certain peculiarities 
of earthquake motion. Whatever immediate success may 
attend these attempts they are to be welcomed as tending 
towards the elucidation of the very difficult physical problems 
the seismologist must face sooner or later. 



CHAPTER XI 

UNFELT SHAKINGS OF EARTH 

Minute Movements. Daily Oscillations of the Plumb. von Rebeur 
Paschwitz. Milne's Theory. Pulsations. Motions due to Distant 
Earthquakes. Comparison of Seismograms. Typical Earthquake 
Record. Preliminary Tremors. Large Waves or Principal Portion. 
Omori's Analysis of Periods. Interpretation of Record. Resonance 
frequent. 

THE invention of the seismograph marked an important 
epoch in the development of seismological science. Some 
idea of the real movement of the ground then became 
possible. Automatic time recorders introduced an accuracy 
quite unattainable in the earlier days. In addition, however, 
to thus making more definite our knowledge of recognizable 
earthquakes, the instruments demonstrated the existence of 
motions and shakings of earth which were too small in their 
amplitudes or too slow in their periodicities to be felt by 
man. 

The first seismoscopes to record unfelt movements were 
lakes and ponds. Thus the great earthquake of Lisbon, 
in 1877, was succeeded by rhythmic movements in Loch 
Lomond, Loch Ness, and in other lakes. These were of the 
nature of forced seiches attributable to unfelt oscillations 
of the ground transmitted from the earthquake source. The 
full significance of this observation was not realized until 
comparatively recent times. 

In 1877, the Russian astronomer, Magnus Nyren, observed 
oscillations in the level of the axis of the transit instrument 
at Pulkova, and these he suggested as having been caused 
by an earthquake which had occurred 1 hr. 14 min. earlier 
at Iquique. Variations of level observed by other astrono- 
mers are now known to be referable to the same cause. 

Meanwhile the Italian seismologists had constructed 
delicately swung pendulums, the practically ceaseless 
motions of which were viewed through a microscope. By 



XI UNFELT SHAKINGS OF EARTH 187 

means of these Tromometers the earliest systematic investi- 
gations into the tremors and pulsations of our earth were 
entered upon. 

Independently and along a different line of development, 
John Milne in Japan had constructed his horizontal pen- 
dulum (described in chapter iv), by means of which he 
began the study of various kinds of earth movements. 
He seems to have been the first to recognize what he called 
slow earthquakes, which could not be felt because of their 
slow periodic motion. As early as 1883 he ventured on 
the statement that ' it is not unlikely that every large 
earthquake might be with proper appliances recorded at 
any point on the land surface of the globe '. 

This prediction began to be fulfilled six years later, when 
a record obtained at Potsdam was recognized as due to 
the same disturbance which produced a fairly strong earth- 
quake in Japan. 

Dr. E. von Rebeur Paschwitz had set up at Potsdam 
a delicate form of horizontal pendulum, with which he 
hoped to detect the gravitational influence of the moon. 
George Darwin, in England, had attempted to solve the 
same problem by means of a very delicate bifilar suspension. 
Both investigators found that there were so many move- 
ments and disturbances taking place that the lunar action 
could not be separated out. From a careful examination of 
the various types of records obtained, von Rebeur Paschwitz 
was led to identify certain of these with real earthquakes 
occurring at a distance. 

When Professor Milne finally left Japan in 1893 he set up at 
Shide in the Isle of Wight the first seismological observatory 
ever established in this country. Hitherto, outside recog- 
nized seismic regions, the installation of instruments as 
seismometers had never been imagined. Now, through the 
agency of the Seismological Committee of the British Associa- 
tion, inspired by its secretary, John Milne, more than fifty 
horizontal pendulums have been set up all over the earth's 
surface ; and from these every half-year there pour in to 
the central station at Shide numerous records of unfelt 
earthquakes. 



188 EARTHQUAKE PHENOMENA XI 

We shall first consider briefly some kinds of motion 
recorded by delicate instruments of the horizontal pendulum 
type. 

One of the most marked features is what is called the daily 
period. Daily oscillations of levels had been from time to 
time observed by astronomers ; but the first to make 
a thorough systematic study of the phenomenon was von 
Rebeur Paschwitz, whose aim, as already mentioned, was 
to measure directly the gravitation action of the moon. 
About the same time Milne in Japan noticed the same 
phenomenon, by means of a light horizontal pendulum 
which had been set up to study tremors. 

To study the phenomenon completely at least two hori- 
zontal pendulums must be set up side by side giving move- 
ments in perpendicular directions, say, north-and-south 
and east-and-west. In some observatories three are used, 
inclined at angles of 60 to each other. It is then found 
that the daily oscillations of the pendulums indicate a slow 
tilting movement of the ground, which might be described 
generally as a rising of the ground on the east and north 
sides from about sunrise till well on in the afternoon, fol- 
lowed by a reverse tilting during the hours of night. The 
range of tilt is generally greater in the EW. direction than 
in the NS. direction, and is more marked in the summer 
months than in the winter months. These are the broad 
features for stations in the northern hemisphere. 

E. Mazelle, in an elaborate paper published in 1900, 1 has 
given a full account of the daily period month by month 
throughout a whole year. No doubt differences in detail 
would be given if another year of months were chosen ; but 
the general character of the phenomenon will probably not 
change materially. I have therefore reproduced on a 
diminished scale the graphical representation of the results 
obtained by him with three Rebeur Paschwitz 's horizontal 
pendulums at Triest. The instruments were installed in 
a cellar with a very small temperature variation, so that 
disturbances due to air currents were reduced to a minimum. 

1 Mitt. d. Erdbeben-Kommission d. kais. Akad. d. Wiss. in Wien. 



XI UNFELT SHAKINGS OF EARTH 189 

From the photographic record given by each pendulum 
the deflections at the successive complete hour marks were 
read off and tabulated hour by hour and day by day through- 
out each month. Hourly means were then formed, and 
from these, corrected for non-periodic changes, numbers 
were obtained giving the average monthly daily periodical 
change for each month. The deviations from the mean of 
each set were finally reduced to angles of tilt, the reducing 




factor being obtained by measuring the period of swing of 
the pendulum. The resultant of the three tilts for every 
hour, after being determined in magnitude and direction, 
was laid off vectorially from a common origin, and a con- 
tinuous curve drawn through their extremities. The exact 
significance of this curve may perhaps be best described 
thus. Imagine a thin rod to be fixed perpendicular to the 
level surface of the ground. Then, in consequence of the 



190 EARTHQUAKE PHENOMENA XI 

daily fluctuation at present under consideration the ex- 
tremity of this rod will describe relatively to the direction 
of the force of gravity a curve similar to the curves shoAvn 
in Fig. 33, or, to speak more accurately, will describe curves 
day by day. the average form of which for each month will 
be as represented. 

In each of the graphs midnight is represented by 24 and 
noon by 12, 6 and 18 representing the intermediate times. 
The arrow heads indicate the direction in which the graph 
is to be described. 

It is evident at once that the oscillation during the colder 
months, November, December, January, and February, are 
much smaller than those of the warmer months, May, June, 
July, August, and September, while the oscillations during 
the remaining months are intermediate to the extremes. 
The peculiar double-looped form of the January graph con- 
trasts strongly with the much simpler forms which are 
characteristic of most of the other months, and indicates 
a pronounced half-daily period associated with the daily 
period. This is also brought out by Mazelle's harmonic 
analysis of the periodicities. 

In order to guard against too much attention being paid 
to the details of the graphs here shown it should be mentioned 
that some of these details are within the errors of observa- 
tion. The greatest range is for the month of June and 
amounts to only one-fiftieth of a second of arc ; and the errors 
of observation will affect the second significant figure of 
the number measuring the deflection. 

There seems to be little doubt that the daily period is 
connected with the heating effect of the sun ; but to explain 
the half-daily period we seem to require to call in the aid 
of tidal action. 

The direct heating effect can hardly be considered as 
really efficient, for, ever since Forbes tested the propagation 
of solar heat downwards through the crust of the earth, 
we have known that the daily variations of temperature 
are cut out at the depth of a few feet, and that the 
annual variation does not penetrate more than 30 or 
40 feet. 



XI UNFELT SHAKINGS OF EARTH 191 

Milne has for many years argued that an important 
factor in the production of the daily oscillation is to be 
sought for in the differential loading and unloading of 
neighbouring areas by solar influences. In the daytime 
evaporation and transpiration from vegetation relieves the 
load, and the ground consequently rises where the solar 
action is more pronounced. This will generate a daily wave 
in the earth's crust facing the sun. Unfortunately this 
explanation does not seem to apply to the southward devia- 
tion which in the warmer months occurs simultaneously 
with the westward deviation. Milne has carried out a 
remarkable series of experiments on the effects of loading 
and unloading in the vicinity of a delicate horizontal pendu- 
lum, and many of the results fit in well with his explanation. 
For example, horizontal pendulums placed on the sides of 
a valley in the Isle of Wight indicate an increased steepness 
on those sides during heavy rain, and a diminishing steep- 
ness during fine weather. The idea is that the precipitation 
loads the valley, causing the bed to sink. During steady 
fine weather the movements at night correspond to those in 
wet weather, evaporation during the day causing unloading 
and the condensation at night the reloading. In other 
words, the valley opens slightly under the influence of the 
sun's heat and closes again during night. Similar effects 
had been previously observed in Tokyo. 

In addition to the slow daily oscillation of the ground as 
measured or at least indicated by the horizontal pendulum, 
there are other movements more or less irregular which are 
usually referred to as tremors or pulsations. Some of these 
are in many cases due to convection currents set up in the 
air of the room or case in which the instrument is placed. 
Others, again, seem to be due to real pulsations of the ground 
set up possibly by winds or barometric changes not neces- 
sarily exactly in the locality where the instrument is. 
Unlike the daily period these pulsations seem to be more 
pronounced in the winter months than in the summer 
months. Thus Mazelle, in his discussion of the pulsations 
at Triest, leaves out of account the five months from 
to September. 



192 



EARTHQUAKE PHENOMENA 



XT 



To show the nature of these pulsations I reproduce a part 
of one of the records obtained by Omori in Japan. 




The motions of which these records are magnifications 



XI UNFELT SHAKINGS OF EARTH 193 

rarely exceed the tenth of a millimeter in range, and are 
usually much smaller. The periods can be estimated at 
once from the record, which contains a time scale marked 
minute by minute on the same sheet. In the part reproduced 
it will be seen that the crests and hollows run about nine 
to the minute. Omori finds that there are two distinct 
periods, the one ranging from 3-4 to 5-7 seconds, and the 
other from 7-1 to 9-3 ; and he points out that these periods 
are particularly prominent in the tremors which come from 
distant earthquakes. The suggestion is that they are 
the periods of vibration natural to the plain in which 
Tokyo lies. 

Attempts to connect these pulsations directly with definite 
meteorological conditions or changes either at the locality 
itself or in the neighbourhood have not been altogether 
successful. Probably several causes are at work modifying 
each other's action, such for example as cyclonic depressions, 
barometric gradients, high winds blowing on mountain chains, 
changes of humidity and rainfall, and even real seismic dis- 
turbances too feeble to be felt. Wiechert has suggested the 
breaking of sea waves on the coast as a cause of pulsations. 

We now pass to the consideration of the propagation of 
earthquake disturbances to great distances. 

When the first records of moderate earthquakes were 
obtained in Japan by Milne, Gray, Ewing, and others, the 
large motion was seen to be heralded by smaller but more 
rapid vibratory motions, which, from their appearance 
on the seismogram, were called ' ripples '. These ripples 
I explained in my paper of 1888 as being in all probability 
due to the elastic vibrations started by the earthquake and 
propagated through the earth's crust at a quicker rate than 
the quasi-elastic vibrations which form the most conspicuous 
part of the felt earthquake. This explanation necessarily 
implies that the further away an observing station is from 
the seismic source the longer will the ripple portion of the 
seismogram be. The beautiful seismograms obtained within 
recent years by Omori by means of his horizontal pendulums 
installed in Tokyo bring out this feature in a very satisfactory 
manner. 

KXOTT O 



194 



EARTHQUAKE PHENOMENA 



XI 



To exhibit it and at the same time lead up to the charac- 
teristics of the seismograms of unfelt earthquakes, I repro- 
duce, on a diminished scale, parts of five seismograms of 
earthquakes which, originating at different distances from 
Tokyo, were felt there as weak shocks. The date and time 
of occurrence of each, and the distance and direction from 
Tokyo of the probable position of the epicentre, are given 
in the following table : 



Date 


Time 


at Tokyo 




23/4/01 

8/5/04 
31/1/01 
24/6/01 

25/8/04 


3h. 
4 
10 
4 
6 


8 m. 30 s. a.m. 
23 49 a.m. 
42 58 a.m. 
6 19 p.m. 
2 31 a.m. 



Epicentre's 

Distance Direction 

from Tokyo 



13km. 

154 

680 
1020 
1030 



S. 15 E. 
N. 33 W. 
N. 33 E. 
S. 44 W. 



The initial portions of the corresponding seismograms 
are reproduced on one sheet, the scale of minute intervals 
being shown alongside ; and the gradual lengthening of the 
preliminary ripples or tremors as the distance of the origin 
from Tokyo increases is evident at a glance. In the seismo- 
gram of April 23, 1901, there is a well-marked undulation 
superposed upon the more rapid oscillations. This feature 
may be seen, although not so clearly marked, in the other 
diagrams. These undulations are no doubt due to the 
natural swing of the horizontal pendulum started by appro- 
priate impulses. As a rule, they die out before the more 
rapid movements disappear, showing that there is no 
continued synchronous motion in the ground itself. They 
decay because of frictional resistances in the instrument. 
As compared with the more rapid movements the slow 
undulations are more marked the nearer the origin is to the 
place of observation. This is quite in accordance with what 
we should expect ; for the nearer the origin the greater the 
chance of an appropriate impulse acting on the instrument. 

These and other similar cases have been carefully analysed 
by Omori, who indicates where he considers the second 
kind of preliminary tremors to begin. It is not always easy 
to see what has guided him in marking the position of this 



XI 



UNFELT SHAKINGS OF EARTH 



195 



point ; and it is doubtful if any such distinction would have 
been imagined if we had not had the records of the unfelt 




FIG. 35. RECORDS OF EARTHQUAKES FELT IN TOKYO. 

motions of distant earthquakes to guide us. To the study 
of these records we now pass. 

o 2 



196 EARTHQUAKE PHENOMENA XI 

First let us look at two other records x obtained by Omori 
in Tokyo. These are due to earthquakes which originated, 
the one in Ceram, and the other near New Guinea. Nothing 
was felt in Tokyo at the times these records were being traced 
out on the revolving cylinder. The instrument which 
recorded them was the same as that used to record the 
movements of the weak felt earthquake of Jan. 31, 1901 
(Fig. 35). The multiplication was 10, giving for the greatest 
range of movement of the heavy weight on the pendulum 
boom the following values : 11-1 mm. in the shock of 
Jan. 31 ; 8-7 mm. in the Ceram shock of 1899 ; 4-3 mm. in 
the New Guinea earthquake of 1900. It may be mentioned 
that other local shocks which were felt gave on the same 
instrument ranges of only 5-6, 5-2, 3-3, and 2mm. The 
reason why these were felt, whereas the Ceram and New 
Guinea shocks were not felt, was largely because of the 
shorter period or quicker motion of the vibrations propa- 
gated from the nearer origin. 

According to Omori, the epicentres of these two earth- 
quakes lay respectively 4410 kms. S. 15 W., and 5570 kms. 
S. 15 E. of Tokyo. As will be seen at a glance, the pre- 
liminary tremors which usher in the large movement are 
extended over a much longer interval of time than in the 
case of the five felt earthquakes already discussed. The 
following are the estimates for the times of duration of the 
preliminary tremors or ripples in these various cases. The 
first row gives the date of the earthquake in Omori's list 
of 1905 ; the second the distance of each epicentre from 
Tokyo in kilometres measured along the surface of the 
earth ; the third the time of duration in minutes of the 
preliminary tremors ; and the fourth the ratio of the 
distance to this time of duration. 



Date of Earthquake 23/4/01 8/5/04 


31/1/01 


24/6/01 


30/9/99 


29/7/00 


Distance in kms. . 13 


154 


680 


1020 


4410 


5570 


Duration in min. . 0-2 


0-3 


1-5 


2-3 


9-4 


12-3 


Dist./Dur. ... 65 


513 


453 


443 470 


453 



With the exception of the first case all these give very 
1 Publications of the Earthquake Investigation Committee, No. 21, 1906. 



XI 



UNFELT SHAKINGS OF EARTH 



197 



similar results for the rate at which the preliminary tremors 
ou trace the larger movements. 




-' 




tf 



Having thus, by consideration of the most recent results, 



198 EARTHQUAKE PHENOMENA XI 

bridged over the interval between the felt earthquake and 
the unfelt, or, as Milne originally called it, the slow earth- 
quake, let us look back at the growth of the new ideas 
which have within ten years transformed the study of 
seismology. Since the publication in 1899 of Milne's book 
on Seismology, in which these ideas were first systematically 
discussed, data have accumulated at an ever increasing 
rate. 

The seismologist is never left long without a reminder 
that the ' solid ground ' on which man builds is in frequent 
commotion. A new improved seismometer is hardly in- 
stalled before a record is obtained of a fleeting oscillatory 
movement, the far-off couriers of a more or less violent 
quake. Milne's indefatigable energies, working through the 
Seismological Committee of the British Association, have 
resulted in the establishment of fully fifty seismological 
stations all over the earth's surface. At each of these the 
Milne Horizontal Pendulum is set up ; and every half-year 
there flows in upon the central station at Shide in the Isle of 
Wight a converging flood of records. If we add to these 
the published records of the important seismological observa- 
tories in Italy, Austria, Germany, Russia, and Japan, we 
have a steadily increasing mass of material ever ready for 
discussion. 

It is now established beyond the possibility of doubt that 
from an earthquake centre disturbances of various types 
spread out and travel with different speeds through the 
body of the earth and over its surface. Views differ some- 
what as to the manner and lines of propagation ; but as 
regards the preliminary tremors which form the first part 
of every record of an unfelt earthquake we must regard 
them ' as due to the propagation along the path of shortest 
time of certain elastic vibrations set up by the initial move- 
ments at the earthquake focus \ l The phrase ' unfelt 
earthquake ' is a convenient expression, indicating that we 
are dealing with a mechanically recorded surface movement 
too small in amplitude and too long in period to be appre- 

1 See ' The New Seismology ', Scottish Geographical Magazine, 1899. 



XI UNFELT SHAKINGS OF EARTH 199 

ciable to our senses at the place where the record is taken, 
but too small only because we are not near enough to the 
origin where the disturbance was in all likelihood a violent 
earthquake. 

The early division of the record was into Preliminary 
Tremors and Large Waves ; and this division still holds, 
but further study has led to the recognition of subdivisions 
of these. Although Rebeur Paschwitz had suggested the 
possibility, Oldham, 1 of the Geological Survey of India, was 
the first clearly to establish the existence in the complete 
record of two distinct phases in the Preliminary Tremors. 
These will be distinguished as P and 8. The entry of the 
Second Phase is usually marked by a sudden increase in the 
amplitude of the sinuous record, and in many cases by 
a longer period. There is frequently some difficulty in 
deciding as to the exact instant at which either phase makes 
its appearance. Similarly there is in many cases a lack of 
precision in the time of commencement of the third phase, 
which marks the initial stages of the Large Waves, or 
Principal Portion as Omori prefers to call it. These points 
should be kept in mind when deductions are being made 
as to the speeds of propagation of the various kinds of 
motion. 

But although there may be difficulty in always determining 
the initial stages of the Large Wave portion, there is no 
doubt as to its marked distinctiveness as a whole. It con- 
sists usually of a series of groups of undulations, each group 
attaining a maximum and being separated from the con- 
tiguous groups by intervening minima. After the last pro- 
nounced maximum the Principal Portion tails off into the 
End Portion, marking the gradual decay of the earthquake 
disturbance. 

From a careful study of the seismograms of unfelt earth- 
quakes obtained in Tokyo, Omori divides the Principal 
Portion into a number of phases, each of which is charac- 
terized by the presence of a fairly constant period and 
a fairly unifojm amplitude. I reproduce a sketch of his 

1 ' On the Propagation of Earthquake Motion to Great Distances,' 
Philosophical Transactions, vol. cxciv, A. 1900. 



200 



EARTHQUAKE PHENOMENA 



XI 



typical earthquake diagram and add his own description of 
some of the phases. 



A/VWVW\/\/\/l 




6L e 



ab 1st Prel. Tremor 

b c 2nd 

cdef..j . . Principal Portion 
End Portion 



cd 1st Phase of princ. portion. 

de 2nd 

.-(/ 3rd ,,] 

.fg 4th 

.{ &c. 
FIG. 37. 



' The Principal Portion denotes the most active part of 
an earthquake, which follows the preliminary tremors, and 
consists of movements of larger amplitude. The earlier 
part of the principal portion is further subdivided into three 
successive stages as follows : (a) the first phase, consisting 
of a few very slow undulations ; (b) the second phase, 
consisting of slow undulations whose period is somewhat 
shorter than in the first phase ; (c) the third phase, consisting 
of vibrations of period much quicker than in the preceding 
two phases. The third phase is followed by others of 
smaller amplitude which may be termed the fourth, fifth, 
sixth . . . phases of the principal portion.' x 

As examples of real records we may take the initial parts 
of the Ceram and New Guinea earthquakes as recorded in 
Tokyo and reproduced in Fig. 36 ; also Omori's records of 
the great Indian earthquake of 1905, and the San Franciscan 
shock of 1906, shown in Fig. 38. On the same sheet I have 
reproduced Davison's record of the Indian earthquake, 
obtained at Birmingham on a horizontal pendulum of 
Omori's type. These are reduced three -sixteenths from the 
originals. A careful study of the diagrams will impress 
upon the mind the characteristics of the unfelt earthquake 
record much more thoroughly than pages of description. 

1 Publications of the Earthquake Investigation Committee, No. 13, 1903. 



XI UNFELT SHAKINGS OF EARTH 201 

The important points brought out by these seismograms 





FIG. 38. 



will be referred to as they arise. The time scale is given 



202 EARTHQUAKE PHENOMENA XI 

by small vertical marks, one minute intervals in the Tokyo 
seismograms, five minute intervals in the Birmingham 
diagram. 

The records obtained on Milne's horizontal pendulum are 
on a much less extended time scale. The instrument, how- 
ever, admirably fulfils the purpose for which it was con- 
trived, namely, the detection of the unfelt earthquake and 
the times of the important phases. Where, as in Milne's 
own observatory at Shide, comparisons are possible between 
the records of different types of horizontal pendulum, the 
more massive type does not seem to have any marked 
advantage over the other in indicating the beginning of the 
record, or in indicating the advent of the large waves. In 
details, however, there are considerable differences, not only 
between records obtained by instruments of different type, 
but also between records obtained by instruments of the 
same type. The elaborate instruments now being installed 
in first class observatories may in time lead to results 
commensurate with their cost ; but so far their indications 
have mainly corroborated those given by the earlier and 
less elaborate forms. 

As regards the character of the record, probably no one 
has analysed it more minutely than Omori. A first glance at 
any one of the records reproduced suggests an almost infinite 
variety of period and amplitude in the sinuosities traced out ; 
but a little attention shows that there is a tendency to the 
recurrence of certain periods. According to Omori's careful 
and laborious analysis not only is this the case, but there 
is also a tendency for certain periods to be more charac- 
teristic of certain phases than of other phases. The follow- 
ing table taken from his paper 1 will indicate better than 
pages of letterpress the real meaning to be attached to the 
general statement quoted above in reference to the typical 
earthquake diagram. The results are average periods 
measured directly from the Tokyo records of eleven large 
earthquakes originating in Alaska, Asia Minor, Mexico, 
West Indies, Central Asia, and East Indies. 

1 Publications of the Earthquake Investigation Committee, No. 13, 1903. 



XI 



UNFELT SHAKINGS OF EARTH 



203 



PERIODS OP VIBRATION IN SECONDS IN THE VARIOUS PHASES OF THE 
EARTHQUAKE RECORDS OF ELEVEN UNFELT EARTHQUAKES 



Preliminary 
Tremors 


Principal Portion of Large Waves 


End 


Phase I 

| 


Phase 2 


Phase 1 


Phase 2 


Phase 3 


Phase 4 


Phase 5 ! Phase 6 


Portion 


1-5(1) 












1 




4-1(6) 


4-8 (2) 


2-9(1) 












7-8(10) 


8-2 (9) 


8-7 (2) 


9-9 (3) 


10-1(1) 


11-7(3) 


9-5(2) 8-1(1) 


9-9 (6) 


13-9 (5) 
18-0(1) 


15-0 (5) 
19-6(1) 




14-1 (1) 


20-4 (9) 


14-9 (5) 
19-9 (2) 


14-3 (6) 


14-5 (4) 


14-3 (3) 
19-8 (4) 





24-8 (3) 






24-0 (3) 




25-0 (1) 


25-0(1) 






30-4 (2) 




27-4 (5) 
















36-1 (3) 


33-7 (8) 


34-3 (1) 










40-3(1) 




44-6 (2) 


42-7 (3) 












| 


54-0 (2) 


















66-0(1) 















The figures in brackets after the number giving the period 
show the number of earthquakes in whose records that 
particular period was detected. If for the moment we 
regard six cases out of eleven as establishing a ' character ', 
we may say that the preliminary tremors are characterized 
by a period of about eight seconds, the second phase of the 
large waves by a period of thirty-four seconds, the third 
phase by a period of twenty seconds, the remaining phases 
by a period of fourteen to fifteen seconds, and the end 
portion by a period of ten seconds. If we take the so-called 
fourth, fifth, and sixth phases as belonging to the End 
Portion, then the characteristic period is still about fifteen 
seconds. 

Again, a broad glance at the general aspect of the table 
shows that the shortest periods are met with in the first 
preliminary tremors, that there is a tendency for somewhat 
longer periods in the second preliminary tremors, that the 
longest periods are encountered in the initial phase of the 
large waves, and that the end portion is characterized by 
periods intermediate between the shortest and longest. 

Similar broad features are given by the analyses of other 
groups of earthquake records, with, however, considerable 
variations in detail. Thus, out of a group of eighty-four 
records of unfelt earthquakes (including five of the eleven 



204 EARTHQUAKE PHENOMENA XI 

mentioned above), the periods which were met with in 
more than twenty of these were as follows : 

4-6 sec. 26 times in First Preliminary Tremors. 

8-7 28 in 

9'3 32 in Third phase of Principal Portion. 

9-6 32 in End Portion. 

13-6 22 in Third phase of Principal Portion. 

From this analysis of one of Omori's tables we may con- 
clude that there is a comparative constancy of period 
characterizing the first preliminary tremors, the third phase 
of the large waves, and the end portion ; but that there is 
not the same constancy of period in the other phases. 

Omori has also discussed in detail the comparative magni- 
tudes of the motions in the various phases. We should 
expect that on the average the larger amplitudes in the 
motion of the ground should be associated with the ^longer 
periods. This, broadly speaking, is what is established by 
Omori's analysis, that is, if we assume that the amplitudes 
given on the seismograms are really proportional to the 
amplitudes of the motions of the ground which are of course 
the original cause of the record. But as we saw in the 
chapter on seismometry this assumption is dynamically 
unsound when the seismometer is not powerfully damped, 
and is in the case of free swinging seismometers approxi- 
mately valid only when the vibrations of the ground are 
distinctly more rapid than the free oscillations of the 
instrument. 

Bearing in mind the conclusions come to in the discussion 
of Seismometry, let us consider some of the outstanding 
features of the seismograms obtained both on Milne's and 
Omori's forms of horizontal pendulums. From our present 
point these differ essentially in the period of swing. In 
Milne's instrument the period is about 12 or 15 seconds, 
whereas in Omori's instruments the period may be as long 
as one minute, and is never shorter than half a minute. 

I am indebted to Mr. Heath of the Royal Observatory at 
Edinburgh for three records (Fig. 39) obtained with the 
Milne Horizontal Pendulum installed there. Two of these 
are reduced copies of the seismograms of the destructive 



UJ 



O 2 



XI UNFELT SHAKINGS OF EARTH 205 

earthquakes of San Francisco and Valparaiso, the latter 
being mixed up with the record of an almost simultaneous 
North Pacific shock. The hours are marked by short white 
strokes. The third is an enlargement of a curious record of 
a small disturbance, which brings out very clearly the effect 
of resonance. The part reproduced is exactly an hour's 
interval. 

About 10 minutes after the first faint tremor the record 
begins to assume a remarkably regular wave-like and approxi- 
mately sinusoidal form, with a period of about half a minute. 
The gradual way in which the amplitude increases and then 
falls away is exactly what would be produced by the influence 
of a steady periodic force of approximately double the period 
of the pendulum. After this has gone on for five or seven 
minutes there is a change of period in the forced vibration. 
As this change is in the direction of an approach to iso- 
chronism the resonance effect becomes more powerful. This 
second vibration has a period of about 18 seconds. Finally, 
with a still shorter period of about 1 3 seconds the amplitude 
of the record opens out much more rapidly, and falls off again 
exactly as Galitzin's curves open out and contract (Fig. 21, 
p. 73). If any definite meaning is to be attached to the 
details of a seismic record, there seems to me to be little 
doubt as to the interpretation in this particular case. There 
has been a slow regular pulsation of the ground (with or 
without tilting it matters not) followed by a somewhat 
more rapid vibration, and that again followed by one still 
more rapid. Each has had time to produce resonance 
effects on the instrument, so that we cannot regard the 
amplitudes as accurately corresponding to the amplitudes 
of the movements of the ground. As the period of the 
ground's motion approaches that of the, free swing of the 
pendulum the resonance works up more quickly, the record 
swelling out more distinctly as the period becomes shorter. 
What is seen to be taking place in this special case will take 
place in the more complex cases when the motions are large 
and irregular. When for a few complete periods the ground 
is moving to and fro with a fairly approximate rhythmical 
motion, then, especially if the period is not very different 



206 EARTHQUAKE PHENOMENA XI 

from the free swing period of the horizontal pendulum, 
resonance will be in evidence, and the horizontal pendulum 
will be itself set swinging, with an amplitude increasing 
at first and then diminishing afterwards. Thus the seismo- 
gram record will be a superposition of the real motion of 
the ground and the forced vibratory motion of the instru- 
ment. A glance at the seismograms reproduced in this 
book will disclose many cases of the kind. When the record, 
beginning small, swells out in a perfectly regular fashion and 
then dies away again, we may be certain that this represents 
not the real motion of the ground, but rather the forced 
motion of the seismometer. This is what has happened in 
the special case under discussion. The period of free swing 
of the horizontal pendulum installed at Edinburgh is 
15-3 seconds, and any period from 10 to 20 seconds will 
undoubtedly produce, if continued long enough, a time 
variation in the amplitude of the kind indicated in the 
seismograms. 

If alongside any particular horizontal pendulum we place 
another with a much longer period of free swing, the records, 
as Imamura showed by direct comparison, will differ dis- 
tinctly in detail. The reason is obvious. Seismic periods 
which will produce evident resonance effects in the pendulum 
of shorter period will have nothing like the same resonance 
effect on the pendulum of longer swing. Compare for 
example the record at Edinburgh of the San Francisco 
shock (Fig. 39) with the record obtained at Tokyo on Omori's 
instrument with a period of 43 seconds (Fig. 38). A strict 
comparison is not possible, seeing that the stations are so 
far apart. But the character of the more open record with 
the more delicate instrument is altogether different from 
that of the less (Jelicate seismometer. In fact, the great 
majority of the periods fall considerably short of 43 seconds, 
and hence the quicker vibrations of the ground will be more 
faithfully recorded on the less stable instrument. 

Nevertheless this instrument also shows in its records 
evidences both of free swing and of resonance. And the 
same holds for the record of the Indian earthquake of 1905, 
which was taken when the instrument had a period of swing 



XI UNFELT SHAKINGS OF EARTH 207 

of 62 seconds. The records are shown much reduced on the 
same sheet (Fig. 38). There can be little doubt, I think, that 
the very large amplitudes shown in both these records are 
mainly instrumental, for the simple reason that their periods 
are almost exactly the periods of free swing of the pendulum 
in each case. Take for example the Indian earthquake. 
In the first preliminary tremors we see not only rapid vibra- 
tions of a few seconds, but also coexisting oscillations whose 
periods are not far removed from one minute. In fact the 
pendulum is trying to swing its own natural swing, and is 
prevented from doing so in a steady manner simply because 
of the complex succession of impulses acting on it. Still the 
free swing, although somewhat broken, is there. Then at 
the point where Omori considers the second preliminary 
tremors to begin, a set of three large waves is produced and 
the periods of these are not very different from one minute. 
Evidently the time integral of the impulse acting just at 
the beginning of this interval has fitted in with the natural 
swing of the pendulum so as to produce a sudden and large 
resonance, and thereafter the free swing so started simply 
decays in time, because of frictional resistances and because 
of the action of forced vibrations not quite in tune. In like 
manner, some 9 minutes later, the motion of the seismo- 
graph pointer begins to work up again exactly as shown in 
Galitzin's curves on page 73. Now if we turn to the record 
of the San Francisco earthquake, we find very similar results, 
except that, the period being somewhat shorter, the large 
wave-like records appearing from time to time have periods 
approximating to that very period. The very large motion 
marking the presence of the Principal Portion might easily 
enough be explained as due to a slow tilting movement, 
producing a large displacement on the boom. The subse- 
quent movements are partly due to the decaying motion 
after the great swing, and on them we see appearing abrupt 
jagged w r avelets which persist for some ten minutes and are 
followed by a more uniform motion having all the charac- 
teristics of a forced vibration with resonance effects. All 
through the record the same phenomenon can be traced, 
not so evidently as in the records of the more quickly 



208 EARTHQUAKE PHENOMENA XI 

swinging pendulums of Milne's type of instrument, but 
none the less certainly. The conclusion seems to be that 
we can place little reliance on the indications of amplitude. 
An appropriate impulse may set up large natural swinging 
in the pendulum, and when that is done it is impossible to 
say anything as to the real amplitudes of the vibrating 
ground. A comparatively small movement of the ground, 
with an appropriate period, may produce on the instrument 
a greater effect than a much larger motion of the ground 
when, with that motion, a very different period is associated. 
A consideration of the highest full line curves in the figure 
on page 80 shows that when the period of the forced vibration 
increases from one-third to one-half of the free swing period 
of the pendulum the effect of resonance will augment the 
amplitude in the ratio of 13 to 11 ; and still greater aug- 
mentations will occur as the period gets nearer the free 
swing period of the pendulum. Even when the forced vibra- 
tion period is not by any means particularly near in value 
to the period of natural swing of the pendulum, a distinct 
resonance effect is nevertheless produced. It may be laid 
down as a general principle that, for periods of forced 
vibration varying from one-third to one-and-a-half times 
the period of free swing of the horizontal pendulum, the 
effects of resonance on the amplitudes are such as to preclude 
us entirely from drawing any sure conclusions as to the real 
magnitude of the earth movements. 

As regards the periods, however, it is quite another matter. 
These are reproduced more or less faithfully in the seis- 
mogram. 

Two interesting remarks are made by Omori in regard to 
the periods which seem to characterize the different phases 
of the motion (see above, p. 203). He finds that the period 
of 4-6 seconds, which is conspicuous in the preliminary 
tremors of records taken in Tokyo, is also a characteristic 
period very prevalent in the pulsations of the ground referred 
to on page 193. The suggestion is that this period belongs 
as much to the stretch of rock and soil on which Tokyo 
stands as to the original disturbance which has come from 
a distance. The disturbance, in fact, throws the region into 



XI UNFELT SHAKINGS OF EARTH 209 

its own natural state of vibration as well as forcing on it 
other periodicities. This view is dynamically sound, and 
is quite in line with what has been already said regarding 
the influence of forced vibrations on the instrument. The 
original earthquake motions produce forced and free vibra- 
tions in the parts of the earth's crust which they invade, 
just as the primary and secondary movements of the ground 
produced in any locality act upon the seismometers installed 
there. 

Another feature pointed out by Omori is the fact that 
seismograms obtained in Tokyo closely resemble one another 
when the original disturbance has come from the same 
region. If this should be corroborated for all centres of 
seismic disturbance, then the seismologist will be able to 
recognize from the appearance of the record the source of 
the shock which has produced it. 



KNOTT 



CHAPTER XII 

SEISMIC RADIATIONS 

Identification of Phase. Relation between Period and Amplitude. 
Selected Data of Kangra Earthquake (1905). Decay of Intensity with 
Distance. Early Tremors killed out. Milne's Method of Fixing Origins. 
Omori's and Laska's Modifications. Milne's World-shaking Earthquakes. 
Milne's and Oldham's Time Graphs. Imamura's Statistical Discussion. 
The Guatemala Earthquake (1902). Oldham's Speculations. General 
Comparison of Times of Transit. Arcual Transmission of Large Waves. 
Approximate Chordal Transmission of Tremors. Fisher's Hypothesis of 
Two Waves in Liquid Interior. Evidence as to Longitudinal and Trans- 
verse Vibrations. Nagaoka's Stratum of Maximum Velocity. Angles of 
Emergence measured by Schliiter. Brachistochronic Paths : Kovesli- 
gethy, Rudzki, Knott, Benndorf. Mathematical Theory compared with 
Observation. Poisson's Ratio satisfied. Energy Distribution. Group 
Velocities. Anomalous Dispersion (Nagaoka). Lamb's Vibration of 
Elastic Sphere. Jeans, Rayleigh, and Love on Stability of Earth. 

JUST as a source of light is a disturbance which spreads 
out as luminous radiations through the ether, so an earth- 
quake is the origin of seismic radiations through the body 
of the earth. In studying the manner of this radiation we 
must compare the records at different stations of one and 
the same earthquake. 

The general character of the earthquake record has been 
considered in the last chapter. Except in very exceptional 
cases the record is characterized by a series of smaller 
quicker movements known as the Preliminary Tremors, 
followed by larger slower movements known as the Large 
Waves. Omori has given a more detailed classification 
into various phases ,basing his division partly on amplitude 
of movement, partly on the periods (see above, p. 200). 
For present purposes, however, it will suffice to recognize 
the First and Second Preliminary Tremors and the Large 
Waves as the great characteristic phases of the record of 
unfelt earthquakes. 



XII SEISMIC KADIATIONS 211 

When the record is obtained at a station close to the 
origin it is not always possible to distinguish the two 
phases of the preliminary tremor ; and the large motion 
follows on in less than a minute. At an earth's quad- 
rant distance from the origin the preliminary tremors 
last some thirty minutes before they are overwhelmed in 
the greater motion of the large waves. The conclusion 
is obvious. We are dealing with a complex set of dis- 
turbances which originate at the seismic focus and radiate 
outwards in all directions with very different speeds of 
propagation. 

To determine these various speeds of propagation we 
must be able to identify the corresponding phases of the 
seismogram obtained at different stations. But this identi- 
fication is not such a simple matter as might at first be 
supposed. Already we have touched on some of the diffi- 
culties of interpretation of the records given by free swinging 
seismometers. Especially disconcerting is the effect of 
resonance, which is not confined as generally imagined to 
cases in which the forcing vibration has a period nearly 
equal to that of the free swinging instrument, but is present 
through a wide range of periods. Looking back to the 
formula given in chapter v, p. 77, we see that, when a slow 
swinging horizontal pendulum is recording a rapid vibration 
of the ground, the amplitude of the forced vibration depends 
not only on the amplitude of the forcing vibration, but also 
on its period. 

Thus if / is the amplitude of the forcing vibration of 
period 2-n/p, and a the forced vibration amplitude imposed 
upon the instrument by a sufficient succession of periodic 
vibrations, then when 2ir/p is distinctly less than 2ir/n, 
which depends on the free vibration period of the instru- 
ment, the relation between a and / is given approximately 
by the formula 



where T is the forced vibration period. 

That is to say, the mere increase in the period of the 
forcing vibration is sufficient to increase the registered 

p 2 



212 EARTHQUAKE PHENOMENA XII 

amplitude on the instrument, although the motion of the 
ground may not have increased. 

No doubt the irregularity of the earthquake motion will, 
except in very exceptional cases, prevent this effect from 
developing to the full extent indicated by theory. Never- 
theless, when the dominant period characteristic of a 
particular phase becomes longer, the tendency must be 
for a greater amplitude to declare itself. Omori, from 
a careful study of seismograms, has established that the 
amplitude does on the whole increase with the period 
throughout a given earthquake record. What theory 
teaches us in this respect is that the amplitude of the record 
may be largely determined by the period of the movement, 
especially in the preliminary tremors. 

In his interesting analysis of the relation of period and 
amplitude in the records of the K.angra earthquake of 1905, 
Omori concludes that the amplitudes associated with the 
different periods increase with the period, reaching their 
average maximum when the period is about 45 seconds. 
This is in accordance with the theory of resonance developed 
in chapter v, if we assume that 45 seconds is not far from 
the average of the free vibration periods of the various 
instruments whose records supply the material. In forming 
his averages, Omori leaves out of account the very large 
deflections which are evidently due to proper pendulum 
oscillation. The effects of resonance, however, show them- 
selves through a great range of periods and not merely in 
the immediate vicinity of the natural free vibration period 
of the seismometer. 

There is as a rule no difficulty recognizing the advent 
of the large waves, and especially that phase of it which 
Omori distinguishes as the third. It seems to mark the 
climax of the movement and to correspond to the period 
during which the energy is most developed. At the same 
time, particularly when the records obtained by different 
instruments are to be compared, the effects of resonance 
will complicate the problem. The maximum amplitudes, 
depending partly on the real amplitudes of earth move- 
ments, partly on their periods, and partly on the periods 



XII SEISMIC RADIATIONS LI:J 

of the free swinging instruments, will occur at different 
parts of the corresponding phases. Occasionally seismo- 
grams of the same earthquake as given by different instru- 
ments bear a striking resemblance to one another ; but 
this is not usually the case. There are differences of detail 
which prevent an accurate identification of phase with 
phase. And even although all the instruments in use were 
mechanically identical, the character of the ground in the 
vicinity of each station could hardly fail to have a modifying 
influence. 

Whatever precision may attend the identification of the 
most energetic phase of the large waves, we cannot with 
the same assurance regard the beginnings of the preliminary 
tremors at the different stations as necessarily belonging 
to the same phase. The decay of energy in the motion as it 
reaches to further distant points will tend to obliterate the 
earlier parts of the preliminary tremors. The instrument 
will begin to record when the movements are sufficiently 
large ; and thus the first appearance of the preliminary 
tremors will be retarded in time as the radiation passes 
out to more distant points. In other words, the speeds of 
transit to distant stations as determined by the advent 
of the preliminary tremors must in general be lower than 
it ought to be when compared to the speeds of transit 
determined from the records of less distant places. It 
seems to me that we have interesting illustrations of this 
retardation in the records of the Indian earthquake of 
April 4, 1905. Omori has collected the data of this earth- 
quake in an important memoir published in 1907 ; and as 
an illustration of the nature of the material at our command 
I reproduce the principal features of the records of twenty- 
eight out of the sixty-nine stations at which records were 
obtained. I have accepted Omori 's estimate both of the 
oentre of the shock and of its time of occurrence at the 
epicentre, although I think his method of using the magneto- 
graph indications at Dehra Dun open to criticism. If we 
place the epicentre somewhat to the north-west of the 
position assumed by Omori, and estimate the time of occur- 
rence nearly a minute sooner than he has done, we get 



214 EARTHQUAKE PHENOMENA XII 

results quite as reasonable on the whole and more in accord- 
ance with the curiously delayed record at Kodaikanal. It 
will be seen in the table that both the first and second 
phases of the preliminary tremors are much retarded at 
Kodaikanal as compared with their advent at Calcutta, 
and yet the distances from the assumed epicentre are only 
as three to two. C. Michie Smith, the Director of the 
Observatory at Kodaikanal, informs me that he is sure of 
his time to a few seconds. Simply to say that the Kodai- 
kanal time is too late does not explain matters. It seems 
to me that this record should have been given equal weight 
at least with the magnetograph record of Dehra Dun. 
The alteration of the epicentre and epoch in the way sug- 
gested will not appreciably affect the results except for 
a few stations near the epicentre such as Calcutta, Bombay, 
Kodaikanal, and Taschkent. For present purposes, how- 
ever, Omori's reckonings may be accepted as a good approxi- 
mation to the truth. 

Accordingly, the epicentre from which the tabulated arcual 
distances of the various stations are measured is assumed to 
be in latitude 31 49' N. and longitude 77 E., and the epoch 
of the earthquake is taken at Oh. 49-8 min. G. M. T. The table 
then gives the times of transit of the preliminary tremors 
(P representing the first and S the second phase) and certain 
phases of the large waves, I corresponding to Omori's first 
phase, L to his third phase, and M to the maximum as it 
appears on the records of Milne's horizontal pendulums. 
L marks the beginning of the most active part of the record. 
The column headed W refers to what is generally accepted 
as the appearance of the large waves after passing round 
the earth by way of the longer arc of the great circle con- 
taining the epicentre and the station corresponding. It 
may be compared with L, the respective times of transit 
of L and W being in the ratio of A to (360 -4), where 
A is the arcual distance of the station. The next column 
gives the maximum amplitude of each record reduced in 
the ratio of the multiplication ratio of the instrument ; 
and the next again the ratio of the amplitudes of L and W. 
The last column contains information concerning the types 




o 
o :c 



XII 



SEISMIC RADIATIONS 



215 



of instrument used the initials referring to the names of 
the inventors, Rebeur-Ehlert, Milne, Omori, Vincentini, 
Wiechert, Stiattesi. 

SEISMIC RADIATIONS 





Arcual 


Transit Times of the Phases 






Station 


Dis- 




\ r,, , 


Instru- 




tance 


P 


8 


I 


L 


Max 


W 


Amp. 


ment 


Taschkent . . . 


11 20' 


2-6 


4-7 


_ 


_ 


7-5 


_ 


5-1 


R-E 


Bombay .... 


13 28' 


3-3 


6-9 










267-2 




M 


Calcutta .... 


13 42' 


2-2 


5-4 


_ 


__ 


_.. 


251-8 




M 


Kodaikanal . 


21 35' 


6 


9-9 















M 


Tiflis 


27 26' 


Q 


10-7 










f)A\ 




Beirut 


34 41' 


8-2 








04.7 




&*-r 

1 Q 




Taihoku (Formosa) 


39 27' 


7-5 


13-6 


19 


23-5 




_ 


i-y 
1-6 


o 


Manila .... 


43 34' 


8-6 


15-3 




26-5 








2-7 


V 


Leipzig .... 


50 16' 


8-9 


15-9 


23-8 


30-3 








1-9 


W 


Tokyo 


51 26' 


9-3 


16-6 


24-3 


32-6 





223-8 


3-1 





Gottingen . . . 


51 45' 


9-1 


16-4 


23-9 


30-5 





235-1 


3-3 


W 


Quarto-Castello . 


51 5h' 


9 


16-2 


23-8 


3M 







2-5 


St 


Mauritius 


55 15' 


9-1 


17-7 


26 












M 


Birmingham 


58 49' 


10-8 


19-1 


26-8 


35-6 





208-5 


0-8 





Shide 


58 52' 


10-8 


16-2 




qo. q 


4.0-9 


990.0 


1M 




Paisley .... 


59 30' 


10-2 


18-5 


_ 


34-1 


40-3 


238-4 


1-4 


M 


San Fernando . . 


66 47' 


12-7 


21-9 





37-2 


44-2 


228-2 


0-88 


M 


Azores .... 


79 54' 


11-2 











64-7 





0-23 


M 


Cape Town . . . 


85 46' 


12-7 


22-7 





46-4 


56-2 


198-5 


0-3 


M 


Victoria (B.C.) . 


97 42' 


17 


24-2 


48-2 


60-5 


67-3 





0-6 


M 


Toronto .... 


101 30' 


16-8 


24-4 


48-2 


60-4 


64-5 





0-4 


M 


Washington . 


105 17' 


18-6 


33-7 


45-8 


61-5 





188-8 


0-6 





Cheltenham . . . 


105 22' 


18-9 


33-6 


45-8 


61-3 





188-5 


0-3 





Honolulu 


108 45' 


14-8 


18-9 






65-7 




0-4 


M 


Samoa .... 


115 08' 


11-6 


29-5 


50-2 


60 




__. 


0-4 


W 


Christchurch . . 


115 03' 


20-2 











157-7 


0-9 


M 


Wellington . . . 


115 45' 


20 


31-1 





70-1 





159-5 


1-3 


M 


Tacubaya (Mexico) 


128 39' 


2H5 


38-3 


54 


72 





178-6 


0-2 






Reduced copies of the seismograms of the Kangra earth- 
quake obtained at some of these stations have been repro- 
duced in Fig. 40. In Fig. 41 an interesting collection of 
seismograms obtained by the Milne form of instrument at 
Paisley has been reproduced by the kind permission of the 
Directors of the Coats 's Observatory. 

The above may be taken as a good example of the kind of 
data the seismologist is called upon to deal with. Glancing 
down the columns we see that the times of advent of the 
different phases become on the average later and later the 
further the station is distant from the origin. There are, 



216 EARTHQUAKE PHENOMENA XII 

however, discrepancies or irregularities which are occasion- 
ally not a little puzzling. 

The best way to bring out the average relations and at 
the same time see where the irregularities are most in 
evidence is to plot the related numbers on section paper, 
and draw by freehand an average curve through the points 
so obtained. Let the arcual distances be measured hori- 
zontally and the corresponding values of the transit time 
vertically. When this is done the various sets of large 
wave points will be found to cluster round straight lines 
which pass through the origin (see Fig. 39). This result 
was obtained by Milne in 1898 (see British Association 
Report for that year), when sufficient material of this kind 
was for the first time collated. But, as was also established 
by Milne in 1898, the preliminary tremor points cannot be 
grouped about a straight line through the origin. The 
time graphs for both phases of the preliminary tremors are 
convex upward, at any rate for the first 90. If we draw 
such a curve through the mean positions up to 100, taking 
into account both Honolulu and the Canadian stations 
(as given by Omori), we shall not find it possible to con- 
tinue the curve so as to pass near the points corresponding 
to the stations at greater distances. Thus the Samoa 
time is much too short and the times in the other cases 
are too long. By neglecting the observations at Ponta 
Delgado (Azores), Cape Town, and Honolulu, Omori is able 
to get a fairly continuous curve passing near most of the 
points. This curve begins convex upwards, but becomes 
perfectly straight from 60 onwards. When, however, we 
study the arrangement of the points as a whole, and especially 
when we bear in mind the evidence derived from other 
earthquakes, Omori's graphical representation seems to be 
open to criticism. It is not a sound scientific method to 
neglect the data supplied by three nearer stations simply 
because they do not harmonize with what is believed to be 
the evidence of nine more distant stations. Moreover, 
a careful study of the seismograms of several of these distant 
stations as supplied in Omori's valuable memoir shows that 
the preliminary tremors began in a very uncertain manner. 



XII SEISMIC RADIATIONS 217 

Take, for example, the Canadian stations Toronto and 
Victoria. The directors of the observatories there marked 
the times of advent of the first preliminary tremors eight 
minutes later than the times which Omori himself made 
out from the records. Probably Omori is right in thus 
correcting the original measurements. There is a very 
slight appearance of an earlier movement ; but the indica- 
tions are extremely uncertain and might be easily enough 
discovered to be some minutes earlier still. Similarly on 
most of the other records from distant stations there are 
the same uncertain beginnings. The movement indicated 
is at the best extremely small, and does not begin in the 
clear abrupt manner so characteristic of records obtained 
at stations within 60 distance from the epicentre. We 
have indeed no assurance that the more distant stations 
obtain records which in their beginnings have point to 
point correspondence with the beginnings of the records 
obtained at nearer places. An earthquake large enough to 
send its tremors all over the world may not be able to trans- 
mit the feebler of these tremors in sufficient intensity to 
be recorded at distant stations. Several undoubted cases 
of rapid transmission to stations approximately antipodal 
to the epicentre will be more valuable evidence in this 
connexion than many cases of apparently slower trans- 
mission. 

Some idea of the rate of decay of intensity with distance 
may be obtained by consideration of the relative amplitudes 
of the records of the same phase of motion at different 
distances. Glancing down the column of amplitudes in the 
table on page 215 we see that in a general way the maximum 
amplitude diminishes as the distance from the epicentre 
increases. But the complexities introduced by resonance 
and the diversities in the character of the soil and in other 
conditions of installation absolutely prohibit us from making 
any quantitative comparisons. There is, however, another 
method to our hand depending upon the fact that with 
sufficiently strong shocks the surface disturbance which 
constitutes the large waves can in many cases be recog- 
nized after having passed through the antipodes and back 



218 



EARTHQUAKE PHENOMENA 



XII 



again towards the epicentre. Presumably, if what are 
symbolized above by the letters L and W refer to the same 
type of movement in its radiation over the surface of the 
earth, similar periods ought to be discoverable in them, 
producing therefore similar effects of resonance on the 
instrument at a given station. We have therefore some 
justification in comparing the maximum amplitudes of L 
and W and in deriving from this comparison the law of 
decay of the surface wave as it spreads out over the 
surface. 

The law of apparent decay will depend on two factors, 
(1) the loss of energy due to friction and viscosity, (2) the 
manner in which wave front expands up to the quadrantal 
distance from the epicentre and contracts thereafter towards 
the antipodal point. Passing through this point it expands 
again and finally contracts as it runs in upon the epicentre. 
But this second factor does not affect the result when we 
compare the amplitudes of the L and W disturbances at 
any one station. From the seismograms published in 
Omori's report I have constructed the following table 
giving the ratio of the maximum amplitudes for L and W 
at four stations ; and it is remarkable how well they agree. 
The first column of numbers gives the minor arcual distances 
from the epicentre, and the second column the major arcs, 
the sum of each pair being 360. The third column con- 
tains the ratio of the amplitudes, and the last column the 
logarithmic decrement of amplitude calculated per degree 
of arc. 



Station 


Arcual Distance 


A 


Minor 


Major 


Tokyo .... 
Birmingham . . 
Cheltenham . . 
Washington . . 


51-4 

58-8 
105-4 
105-3 


308-(> 
301-2 
254-(5 
254-6 



Ratio of 
Amplitudes 


Coefficient 
of Decay 


50 
60 
14 
12 


0-015 
0-017 
0-0175 
0-017 



The calculation is made on the usual assumption that the 
amplitude falls off according to the exponential law. Thus 
if A and a represent the amplitudes respectively of the 



XII SEISMIC RADIATIONS 219 

L and W disturbances at a station whose arcual distance 
is x from the epicentre, then the ratio 

A 

_ =e (;jco-2.r) 

a 

where e is the number 2-71828. 

With this value of k> namely, 0-017, we find that the 
amplitude of the movement is cut down to half its amount 
at a distance of 41- 2. 

This seems to me to be a fact of considerable importance. 
We cannot escape from the certainty that similar though 
possibly smaller rates of decay will rule in the other kinds 
of motion transmitted. It is consequently not surprising 
that the first appreciable tremors of the preliminary phase 
should be retarded in time at certain of the more distant 
stations. When these first indications come on with an 
almost imperceptible but gradually increasing movement, 
we should in most cases be justified in regarding the com- 
mencement as uncertain and probably delayed. 

This killing out of the early tremors will no doubt be 
more in evidence in some regions than in others. The 
nature of the underlying soil and rocks will be a deter- 
mining factor. Thus there seems to be a tendency for the 
Canadian stations to give records which have a retarded 
commencement. My own suspicion is that the times 
originally given by Mr. Baynes Reid at Victoria (B. C.) 
and by Professor Stupart at Toronto really refer to the 
advent of the second phase of the preliminary tremors. 
Also a careful inspection of the Cheltenham (U. S.) and 
Washington seismograns shows that the second phase 
might have begun about five minutes sooner than the 
times chosen by Omori. Occasionally, indeed, it is not very 
obvious what considerations have led to the identification 
of the second phase. The mind seems to be unconsciously 
led to fix upon the time from a certain expectation as to 
when it ought to be. 

There is again the early arrival of the preliminary tremors 
at Cape Town, the Azores, and Honolulu. This may be 
explained as due to pulsations coexisting with the true 



EARTHQUAKE PHENOMENA XII 

seismic vibrations. But it is also conceivable that at these 
stations the rapid tremors are not so quickly killed out, 
perhaps because they are in more continuous material touch 
with the inner substance of the earth. 

There are indeed so many factors to be considered that 
we cannot expect to get all we want from one particular 
earthquake. We must compare the results of a great 
number. 

As already pointed out, Milne was the first (in 1895) to 
discuss generally the relations between distance and times 
of transit of the preliminary tremors and the large waves : 
and in 1898 (see British Association Report) he showed how 
origins could be approximately determined from a knowledge 
of the interval of time by which the large waves were 
outraced by the preliminary tremors. When we know 
this difference for two stations we can by means of a little 
arithmetic and the laying off of two arcs on a globe obtain 
two points of intersection near one of which the origin 
will be. Our knowledge of the seismic regions of the globe 
enables us in general to choose one of these as the epicentre. 
Indeed this knowledge enables us not unfrequently to infer 
the whereabouts of the origin from inspection of one seismo- 
gram only. Using the results from three stations we get 
the epicentre at once as the approximate intersection of 
three arcs. 

Omori's method of locating the epicentre is the same 
in principle. By combining the records of a number of 
earthquakes he finds that the distance of the epicentre 
from a station whose record gives t seconds for the duration 
of the preliminary tremors before the advent of the large 
waves may be expressed by the formula 

Distance in kilometres = 17-U 1360. 

Strictly speaking, the formula holds for durations lying 
between four and eleven minutes, that is between 25 and 
90 arcual distance. When the duration of the first 
preliminary tremors only is taken into account the formula is 

Distance = 6-54J + 720. 
Omori has used these formulae in fixing the position of 



XII SEISMIC RADIATIONS 221 

epicentres not very distant from Tokyo. For more distant 
earthquakes the linear relation breaks down. 

A similar formula has been elaborated by W. Laska, 1 
who has also added an obvious but laborious mathematical 
method for calculating the position of the epicentre from 
the three distances estimated by means of the formula. It 
is very doubtful if the accuracy of the data is sufficient to 
repay the labour of undertaking this calculation. In any 
case a linear formula applies only within a limited range, 
whereas Milne's original method takes direct account of the 
time curves. With these as guide the laying off of arcs on 
a good sized globe is at present to be preferred. 

Milne has systematically applied this method to the deter- 
mination of earthquake origins since 1900 ; and beginning 
with the year 1902 he has prepared for the British Associa- 
tion Report, year by year, a map giving the total number of 
large earthquakes which have originated since 1899. The 
map, bringing the statistics down to the end of 1906, is 
reproduced in chapter vi, p. 97, where also will be found 
a description of the areas and numbers marked on it. 

In the table following I have arranged the main facts 
contained in Milne's maps, so as to show the total number 
of large earthquakes which have originated in the several 
districts since the method began to be applied, and also the 
annual addition to this total year by year since 1901. It 
will be noticed that all the districts in which the earthquakes 
originate are essentially oceanic or littoral, except district K r 
which runs from the south-east of Europe to the Himalaya 
mountains. A, B, D lie on the west coast of the Americas, 
beginning at Alaska ; C includes the West Indies ; E is the 
Japan district, and F the East Indies region. G lies in the 
Indian Ocean ; H, I are in the North Atlantic ; J is in the 
Arctic regions, and L in the Antarctic. The district M was 
introduced to take into account the earthquake tremors 
which were recorded by the scientific staff of the Discovery 
in her visit to the Antarctic regions in 1902. There is some 
doubt as to the meaning of the records obtained by the 

1 See Mitteilungen der Erdbeben-Kommission of the Vienna Academy of 
Sciences (1903). 



222 



EARTHQUAKE PHENOMENA 



Xll 



Discovery ; some may have been due to the shakings of the 
ice quite apart from real seismic disturbances. They are 
entered in the table, but are not taken into account in the 
general discussion. 

MILNE'S LIST OF LARGE WORLD-SHAKING EARTHQUAKES 





Totals since 1899 to 


Number each Year 






1901 


1902 


1903 


1904 


1905 


1906 


1902 


1903 


1904 


1905 


1906 


A 


25 


27 


30 


30 


32 


34 


2 


3 





2 


2 


B 


14 


22 


28 


28 


32 


36 1 


8 


6 





4 


4 


C 


16 


22 


25 


25 


25 


29 


6 


3 




4 


D 


12 


15 


16 


16 


16 


20 


3 


^ 





4 


E 


29 


38 


45 


59 


67 


85 


9 


7 14 


8 


18 


F 


41 


55 


66 


75 


94 


115 


14 


11 | 9 


19 


21 


G 


17 


18 


21 


21 


22 


23 


1 


3 


1 


1 


H 


22 


22 


24 


25 


28 


31 





2 i 1 


3 


3 


I 


O 


3 


5 


5 


5 


5 





2 1 








J 


3 


3 


o 


3 


3 


3 




; 








K 


14 


36 


58 


62 


77 


91 


22 


22 4 15 


14 


L 


2 


2 


2 


2 


2 


2 

















M 










(75) 


(75) 


(75) 


- 





| 







198 


263 


323 


351 


403 


474 


65 


60 


28 


52 


71 


Annual 
Average 


66 


65-8 


64-6 


58-5 


57-6 


59-3 













The most active districts are E, F, and K, which lie close 
to and within the great Asiatic continent. The North 
American districts A, B, and C are more energetic seismicalty 
than the South American district D. Clearly, extent of 
stretch of continent has an important bearing on seismicity 
as well as height of land above ocean depths. The earth- 
quakes originating in H were comparatively small, although 
in number they exceed those of D. 

There is a marked minimum activity in the year 1904. 
The records do not go quite far enough back to indicate 
whether there was a maximum in 1900 or 1901. The 
averages hint at the existence of a maximum in either of 
these years. The year 1901 was a year of minimum sun- 
spot activity. It would be curious indeed if minimum solar 
activity should be accompanied with maximum terrestrial 
seismic activity. 



XII SEISMIC RADIATIONS 223 

There is no doubt that the year 1906 impressed the 
imagination as a year of special activity. This was because 
several of the world-shaking earthquakes occurred in civilized 
and densely populated regions. It will be noted, however, 
that the districts B, C, and D, within which San Francisco, 
Kingston, and Valparaiso respectively lie, were not particu- 
larly active ; the great increase in the number throughout 
the year 1906 occurred in districts E and F, especially in 
the former. The origins must have been well out to sea, 
for Japan itself was not visited by any destructive seismic 
disturbance. 

District G is credited only with one earthquake origin in 
1906. This district, indeed, which in 1901 appeared to be 
as important a seismic region as district K, has steadily 
fallen behind during the succeeding years. It is possible 
that the early statistics utilized by Milne were not so 
accurate as the later ones, and that we may have to con- 
sider district G as of relatively small importance. 

With the accumulation of statistics year after year, the 
earlier results obtained by Milne have been in the main 
corroborated. In 1900 Oldham l discussed the data of seven 
large earthquakes, and drew the time-curves for the first and 
second preliminary tremors, and also for the commence- 
ment and maximum of the large wave portion. With still 
fuller statistics Milne in the British Association Reports for 
1902 gave average time-curves which are shown in Fig. 4'2. 
Each dot or cross represents one result from a particular 
earthquake. 

The arcual distances of the stations from the seismic focus 
in each earthquake for which records were obtained are 
measured horizontally, and the corresponding times of the 
respective motions reckoned from the epoch are measured 
vertically. The points so obtained cluster along and around 
three lines. In the case of the large wave maximums the 
line is practically straight, showing that this maximum 
phase in all probability passes through the earth's crust 
close to the surface, with an average speed of 95 per hour, 

1 'Propagation of Earthquake Motion to Great Distances,' Philosophi'ul 
Transactions, vol. 194. 



224 



EARTHQUAKE PHENOMENA 



XII 



or l-6 per minute. If we take the averages of the various 
rates of transit in the case of the Kangra earthquake we 
find that the first phase, I, the third phase, L, and the 
maximum, M , passed through the crust close to the surface 

139 r 



/2S 

f!C 



115 

HO 
105 
IQO 
95 
30 

es 

80 
7S 

70 



55 

so 

45 

40 

25 
30 
25 

20 

5 



10 10 JO 40 50 60 70 6O 30 (00 110 120 /JO 140 ISO J60 //<? /60 130 200* 

Degrees 

First phase or preliminary tremors Second phase x Large waves -f 

FIG. 42. MILNE'S TIME-CURVES. 

with the respective speeds of 2-18, 1-71, and l-46 per 
minute. It thus appears that the large wave seismic 
radiations of the Kangra earthquake passed a little more 
slowly through the crust than the average for the cases 
considered by Milne. 




XII 



SEISMIC RADIATIONS 



225 



The lines representing the average time-curves for the first 
and second phases of the preliminary tremors are distinctly 
not straight. The curves seem to tend towards a maximum 
as they approach the arcual distance of 180. 

These waves pass through the earth by brachistochronic 
paths, that is, paths of shortest time, the form of which de- 
pends on the manner in which density and elasticity vary 
with depth below the surface. 

In the British Association Report for 1902 I pointed out 
that the form of Milne's time-curves at once suggested a very 
approximate chordal transmission. This is brought out in 
the following table, which is a modification of that originally 
given in the Report. The first column gives the arcual 
distances, the second and third the average times of start of 
the two phases of the preliminary tremors, the fourth and 
fifth the chords and arcs in terms of the earth's radius as 
unity, and the remaining columns the corresponding chordal 
and arcual speeds of the two phases in earth-radius per 
minute. This mode of expressing the speed has the con- 
venience that the same unit is employed in each. We can 
easily pass to miles per second or kilometres per second by 
multiplying respectively by 66 and 106. 

CHORDAL AND ARCUAL SPEEDS OF P AND S PHASES OF PRE- 
LIMINARY TREMORS IN EARTH-RADIUS PER MINUTE 



Arc 


Times 


Chord 


Arc 


Chordal Speeds 


Arcual Speeds 


P 


S 


P 


S 


P 


S 


20 


4 


6-9 


0-34 


0-35 


0-087 


0-050 


0-087 


0-051 


40 


8 


13-3 


0-68 


0-70 


0-086 


0-051 


0-087 


0-052 


60 


114 


19 


1 


1-05 


0-088 


0-053 


0-092 


0-055 


80 


15 


23-0 


1-29 


1-40 


0-086 


0-054 


0-093 


0-058 


100 


17-7 


27-8 


1-53 


1-74 


0-086 


0-055 


0-099 


0-063 


120 


20 


30-3 


1-73 


2-09 


0-087 


0-057 


0-105 


0-069 


140 


21-7 


32-1 


1-88 


2-44 


0-087 


0-059 


0-113 


0-076 


160 


22-2 


32-9 


1-93 


2-79 


0-087 


0-059 


0-126 


0-085 



These numbers indicate that the transit speeds of the pre- 
liminary tremors measured as along the arc increase with 
the distance. Whatever may be the form of the brachisto- 
chronic paths which all such vibratory motions necessarily 



KNOTT 



Q 



226 EARTHQUAKE PHENOMENA XII 

pursue, they certainly do not confine themselves to the crust 
through which the large waves are propagated. The re- 
markable constancy of the speed of the first preliminary 
tremors, estimated as if transmitted along the chord, sug- 
gests that the brachistochronic paths cannot deviate far 
from the chords through the greater part of their course. 
The same constancy does not characterize the second pre- 
liminary tremors. A comparison of their arcual and chordal 
speeds shows, however, that the paths come nearer to the 
chordal position than to the arcual. 

The broad conclusions which may be drawn from these 
earlier results are that the large waves are propagated 
round the immediate interior of the earth's crust, like 
sound round a whispering gallery, with a speed of 1-85 miles 
or 3 kilometres per second ; that the first phase of the 
tremors is transmitted across the earth's diameter with a 
speed of 5-7 miles or 9-17 kilometres per second ; and that 
the second phase passes across the same diameter with 
a speed of 3-9 miles or 6-25 kilometres per second. 

Some of the conclusions just indicated are not accepted 
by the Japanese seismologists. Omori considers that all 
types of wave are transmitted arcually, not necessarily 
along the surface, but along appropriate arcual layers 
parallel to the surface. The general idea is that there is 
a speed peculiar to each layer, and that there is a particular 
layer of maximum velocity along which the preliminary 
tremors are transmitted. In No. 16 (1904) of the Publica- 
tions of the (Japanese) Earthquake Investigation Committee, 
Imamura has brought together a large amount of material 
in support of this view. No fewer than eighty-five earth- 
quakes are discussed ; but in regard to the debated question 
of the transit speed of the preliminary tremors, the great 
majority of these are, on the author's own admission, of 
absolutely no account. The origins of only fifteen of them 
were definitely kno.wn ; in all other cases the origins 
were estimated by comparisons of the seismograms at 
different stations. This method is sufficiently satisfactory 
for ordinary purposes ; but it can hardly be accepted as 
a trustworthy basis for a sound scientific argument as to the 



XII SEISMIC RADIATIONS 227 

speeds of propagation of the various phases of the earth- 
quake motion. But a much more serious objection to Ima- 
mura's method is that in all but three or four cases he has 
estimated the epoch of the earthquake at the origin on the 
assumption of what he wants to prove, namely, the arcual 
propagation of the preliminary tremors. Indeed, it cannot 
be too strongly urged that those earthquakes only whose 
epochs are known definitely to within a minute are of any 
value in an investigation of this kind. It is not always 
possible to get this information, especially if the origin is 
under the ocean. Even in cases where the origin is under 
the land there is frequently difficulty in timing the exact 
occurrence of the quake, chief y because of the lack of accu- 
racy in the measurement of local time. 

The most complete of all the cases discussed by Imamura 
is the Guatemala earthquake of 1902. Oldham 1 has criti- 
cized the methods and conclusions of the Japanese seismo- 
logist, and has brought together all the possible material 
available for a complete study of the transit velocities of the 
first and second tremors and of the large waves. He shows 
that Milne's original estimate of the epoch (2 h. 22m. G.M.T.) 
is more accurate than that adopted by Imamura, namely, 
2 h. 26 m. This difference of four minutes will affect con- 
siderably the estimated speed of propagation, and will quite 
destroy the linearity of the time graph of the first tremors 
regarded as a whole. Forty-six of the sixty-one individual 
records collected by Oldham are grouped together according 
to distance in seven average groups. Dividing the arcual 
distance of each average group from the origin by the corre- 
sponding time reckoned from the epoch, Oldham finds that 
this ratio increases with the arcual distance. 

I have discussed the data in a different way. Assuming 
a linear relation between the time and the distance, arcual or 
chordal as the case may be, I have worked out, by the 
method of least squares, the coefficient of each term. Calling 
the arc 6, and the chord x, and representing by ^ and t. 2 
the times respectively of the first tremors and the large wave 

1 ' The Great Guatemala Earthquake,' Proceedings of Royal Society, 1905. 

Q2 



228 EARTHQUAKE PHENOMENA XII 

maximum reckoned from the epoch of the earthquake, I 
find the relations to be as follows : 

First Tremor Large Waves' Maximum 

6 = 0-319+0-134^ =0-0066 + 0-0302Z 2 

x = 0-097 + 0-0976^ x = 0-3062 + 0-0185^. 

The first term in each expression shows to what degree of 
approximation the times and distances can be regarded as 
strictly proportional. The smaller this term the better the 
approximation. Evidently the chord formula is better for 
the first tremors, and the arc formula for the large waves. 
There is no question as to the mode of propagation of the 
large waves; the chord or x formula is meaningless, de- 
manding an epoch about seventeen minutes earlier than the 
true epoch. But it is the chord formula which best suits the 
first tremors, the arc or 6 formula demanding an epoch 2-4 
minutes later than the true epoch. 

The coefficient of t in each represents the speed of pro- 
pagation in earth-radius per minute. Hence the first tremors 
are propagated with the average chordal speed of 6-4 miles 
per second or 10-3 kilometres per second ; while the large 
waves' maximum is propagated with an arcual speed of 
2 miles per second, or 3-2 kilometres per second. 

In a recent paper on the Constitution of the Interior of the 
Earth 1 Oldham has considered with great care the returns 
for twelve earthquakes, for most of which the origins and 
epochs were known with fair accuracy. Six of these origi- 
nated in or near Japan, and the others in Argentina, India, 
Turkestan, the Philippines, Guatemala, and Kashgar. Un- 
fortunately four of the Japanese earthquakes had their 
origins well out to sea, so that their positions were matter 
of inference only. From these inferred distances which 
might easily be in error by 50 to 100 kilometres the epochs 
were obtained on the assumption that the disturbance which 
was felt in Japan travelled at the rate of 3 kilometres per 
second. This, however, is at best an average ; and even if 
the time observations themselves were above criticism this 
way of estimating may easily cause an error of half a minute 
1 Quarterly Journal Geological Society, 1906. 



XII 



SEISMIC RADIATIONS 



229 



or more. But in the discussion of the transit speed of the 
first preliminary tremors the great majority of the time 
intervals which fall to be considered vary from six to 
fifteen minutes. In such a case an error of half a minute is 
proportionately large. 

There can be no doubt, however, that Oldham has made 
the most of the material to hand, and that his results may be 
accepted as the best averages so far obtained. 

I propose now to embody in one comparative table the 
times of transit for various distances as given by Milne, 
Oldham, and by the returns for the recent earthquakes of 
Kangra and San Francisco. I have also added the averages 
prepared by G. B. Rizzo, 1 who has charge of the seismological 
observatory at Messina. These occupy the third column of 
times of transit as given in the following table. The first 
three columns of average times are headed by the initials of 
the authorities named. The numbers for the Kangra (K) 
and Californian (C) earthquake are those compiled by 
Omori. 

TIMES OF TRANSIT IN MINUTES 



Arc 


First Preliminary Tremors 


Second Preliminary Tremors 


M 


O 


R 


K 


C 


M 





R 


K 


C 


20 


4 


4-2 


4-5 


4-6 


4-3 


6-9 


7-4 


8-5 


8-5 


8-8 


30 


6-5 


6 


6-1 


6-4 


6-3 


10 


11 


11-2 


11-3 


11-8 


40 


8 


7-9 


7-4 


7-9 


8-1 


13-3 


13-7 


14 


13-9 


14-5 


60 


11-5 


11 


9-7 


10-5 


11-5 


19 


19 


18-6 


18-9 


19-2 


80 


15 


14 


11-9 


13 


12-9 


23-9 


23-2 L>3-S 


24-7 


26-2 


90 


16-2 


15 


13 


14 


14-3 


26 


24-7 26-4 


27-5 


24-9 


100 


17-7 


16-3 


14-1 


f 15-21 

18 ) 


16 


27-8 


26-4 


31-4 


30-6 


26-5 


120 


20 


18 


16-3 


20-5 


19? 


30-3 


29 


33-6 


36-2 


32? 


140 


21-7 


20 


18-6 








32-1 


181-6} 

143-21 


38-6 


_ 





150 


22-2 


21 


19-7 








32-7 


45 


41-8 








160 


22-2 


21-3 


20-8 








32-9 


46-3 i 44-8 


_ 


: 


180 





22 


23 











50 49-5 









In the British Association Report for 1903 Milne gave 
reasons for a considerable correction to be applied to these 



1 Sulla Propagazione dei Terremoti, Accad. Reale d. Scienze di Torino, 
(1907). 



230 EARTHQUAKE PHENOMENA XII 

times of transit. This will be discussed later. Meanwhile 
we take the data as they are given in the table. 

Rizzo's times of transit increase regularly by 1-1 minute 
for every 10 increase of distance from 60 upward. This 
regularity does not appear in any of the other columns, 
whether these refer to averages or single earthquakes. Taking 
the numbers as they stand we observe that, on the whole, 
there is a tendency for the later data to indicate, in the case 
of the first phase, a time of transit distinctly shorter for the 
moderately distant stations than was indicated by the earlier 
data discussed by Milne and Oldham. This is specially 
marked in the neighbourhood of the quadrantal distance. 
At the same time there is no such indication in the case of 
the second phase. The most obvious explanation of this i& 
the increasing number of stations equipped with the most 
delicate types of seismometers. It is in Europe mainly that 
this great development has taken place ; and Europe happens 
to be just about the quadrantal distance, more or less, from 
many centres of world-shaking earthquakes. With more 
sensitive instruments the first beginnings of the earthquake 
tremors will naturally be observed sooner. But once the 
tremors are sensible on the seismometer record the advent of 
the second phase will not be so influenced by the sensitiveness 
of the instrument. 

The times of transit for the distance 180 cannot be trusted, 
inasmuch as they have been obtained by a process of extra- 
polation. There is only one case I know of in which a distinct 
record was obtained at a distance approaching 180. This 
was the Caracas earthquake of October 29, 1900. Batavia, 
according to Imamura's list, was distant 175 from the epi- 
centre ; but I have no information regarding the epoch of 
the shock. We find, however, that the record began at 
9 h. 32-4 m. at Batavia, and at 9h. 20-9 m. at the distance of 
60 (mean of two). Taking 10-5 as a fair mean value of the 
time of transit to the latter distance, we find for the probable 
time of transit to a distance of 175 the value 22 minutes. 
This agrees with Oldham's estimate for 180, and may be 
taken as the best uncorrected value obtainable. 

The second phase is very difficult to identify in seismo- 



XII 



SEISMIC RADIATIONS 



231 



grams obtained at distant stations ; and it is doubtful if we 
are in a position to say anything definite as to the time of 
transit for distances greater than 150. 

Taking all circumstances into consideration, we may accept 
Oldham's average values for the first phase as the most trust- 
worthy. If following the lead of the Kangra and San Fran- 
cisco earthquakes we decrease the times of transit to approxi- 
mately quadrantal distances, but adhere to Oldham's values 
for greater distances, we get results which at once suggest 
retardation of the first appearance of the tremors. On 
forming the time graph after the manner of Milne's chart, 
we find that the curve giving time in terms of arcual 
distance begins convex upward, then becomes flattened out 
or even concave upward in the neighbourhood of 90, and 
finally finishes with an upward convexity. Oldham's curve 
is convex all the way, with a slight break in the continuity 
of curvature at about 140. 

I now reproduce Oldham's condensed table of averages, 
treated in the manner in which I have treated Milne's results 
above (p. 225). 



OLDHAM'S TIMES OF TRANSIT OF EARTHQUAKE TREMORS AVERAGED 

FROM TWELVE EARTHQUAKES. SPEEDS IN EARTH-RADIUS PER 

MINUTE 



Arc 


Times 


Chord 


Arc 


Chordal Speeds 


Arcual Speeds 


P 


S 


P 


S 


P 


S 


20 

60 
90 
120 

150 
180 


6 
11 

15 
18 
21 
22 


11 

19 
25 1 
29 
45 
50 


0-518 
1-00 
1-41 
1-73 
1-93 
2-00 


0-524 
1-05 
1-57 
2-09 
2-62 
3-14 


0-086 
0-091 
0-094 
0-096 
0-092 
0-091 


0-047 
0-053 
0-057 
0-060 
0-043 
0-040 


0-087 
0-095 
0-105 
0-116 
0-125 
0-143 


0-048 
0-055 
0-063 
0-072 
0-058 
0-063 



The chordal speeds are not so steady in value as in the 
case based on Milne's averages ; but indeed the values 
obtained from Milne's statistics were too regular to satisfy 
a true chordal transmission. For we know that the speed of 
transmission is certainly less in the upper than in the lower 
parts of the crust. In coming out to the surface the ray of 



232 EARTHQUAKE PHENOMENA XII 

disturbance must pass through these upper layers. The 
average speed is all that we can get from the data ; and since 
proportionately more of the upper crust is passed through the 
less distant the observing station, it is clear that the average 
speed will fall short of the speed in the deeper regions by 
an amount which will be greater for the nearer station. Thus 
the increase in the chordal speeds as the distance increases 
up to 90 is what we should expect for the case of an approxi- 
mately chordal transmission. After 120 there is a distinct 
fall off in the average chordal speed. I believe this fall off 
to be due to high emergence angles and to energy distribu- 
tion as explained below (pp. 249, 255). 

Up to 120 Oldham's delineation of the time graph of 
the second phase does not differ essentially from his earlier 
delineation or from Milne's representation given above. 
Milne gives three points above 120 distance, and these 
imply a continuation of the curves roughly resembling the 
form of the graph for the first phase. Oldham, however, 
gives eight points on the graph at distances greater than 
130 ; and these lie so much higher than the points for 
smaller distances that it is not possible to draw a con- 
tinuous curve through them all. This peculiarity is indi- 
cated in the table by the abrupt fall off in the estimated 
average speed of transmission of the second phase tremors 
for the two highest distances tabulated. Assuming this 
discontinuity to be a real effect Oldham proceeds to explain 
it on the hypothesis of an inner core of the earth trans- 
mitting vibrations at a distinctly slower rate than the 
surrounding shell. His argument is as follows : 

' As regards the size of the core, we have seen that it is 
not penetrated by the wave-paths which emerge at 120 ; 
and the great decrease at 150 shows that the wave-paths 
emerging at this distance have penetrated deeply into 
it ... Now the chord of 120 reaches a maximum depth 
from the surface of half the radius ... so that it may be 
taken that the central core does not extend beyond about 
0-4 of the radius from the centre.' 

His conclusion, which may be easily verified, is that the 
rate of transmission through the core is just about half that 



XII SEISMIC RADIATIONS 233 

through the shell. This ingenious hypothesis requires that 
the seismic rays on entering the core will suffer considerable 
refraction, very similar to but more marked than the re- 
fraction of rays of light through a spherical lens of glass 
or crystal. The law of refraction depends on the ratio of 
the speeds of propagation in the two media, and the speed 
of propagation depends (see chapter viii) on the square 
root of the ratio of the elastic modulus to the density. 
But it will be noticed that the time graph for the first 
tremor phase does not show the same discontinuity. There 
is a slight sag in Oldham's curve as drawn, but it is too 
slight in itself to serve as basis for a serious argument. 
Why then should the one set of disturbances be powerfully 
influenced by the assumed central core, and not the other 
set ? An explanation may, of course, be given on two 
further assumptions. First, the elastic modulus which 
determines the propagation of the first phase may vary 
very nearly proportionately to the density for all parts of 
the earth ; secondly, the elastic modulus on which the 
transmission of the second phase depends may, on the other 
hand, vary with depth below the earth's surface according 
to a law quite different from that which holds for the density 
changes. Now the densities are the same for both types of 
disturbance. Hence the marked difference in the behaviour 
of the two phases must be ascribed to the manner of change 
of the elastic moduli ; and we are driven to the extremely 
improbable conclusion that one elastic modulus changes 
slowly and continuously with depth, while the other becomes 
suddenly reduced to one quarter of its value in the outer 
shell. Considering the great difficulty in many cases of 
distinguishing the exact advent of the second phase in 
seismograms of small intensity, we can hardly regard 
Oldham's hypothesis as at all convincing until a great many 
more observations are to hand. In this discussion it does 
not seem to me that due attention has been paid to the 
distribution of the energy of the radiations as they are 
transmitted outward from the earthquake focus. 

The data on which Oldham bases his ingenious hypothesis 
of the inner nucleus of the earth are, indeed, altogether too 



234 EARTHQUAKE PHENOMENA XII 

meagre. We are hardly yet in a position to construct such 
a definite picture. With regard to the probable nature of 
the second preliminary tremor as distinguished from the first, 
the simplest idea undoubtedly is that we have to do with 
two types of waves whose speeds of propagation across 
the substance of the earth are different. If we assume 
that the earth as a whole behaves like an elastic solid these 
radiations of seismic disturbance may be compared to the 
compressional and distortional waves discussed in chapter x. 
The recognition of the two types has indeed been regarded 
as a strong argument in favour of the solidity of the earth. 
But if, as many still believe, the earth is essentially fluid 
throughout, how are the two types of wave to be ex- 
plained ? 

The Rev. Osmond Fisher, whose treatise on the Physics 
of the Earth's Crust presents in a masterly manner the 
argument in favour of the fluidity of the earth, has shown 
how the difficulty may be met. 1 His fundamental con- 
ception is that beneath the solid crust of the earth, estimated 
to be some eighteen or twenty miles thick, there is a molten 
magma containing gas in solution. Henry's law of the 
absorption of gases by liquids is assumed to hold, namely, 
that the mass of gas dissolved is proportional to the pressure. 
Since at ordinary temperatures and pressures gases obey 
Boyle's law, Henry's law may for such cases be stated 
thus : The volume of a gas which may be absorbed by 
a given volume of the liquid is independent of the pressure. 
This is the form in which Fisher applies it to the case of 
molten rocks under pressures of several thousands of atmo- 
spheres. On this insecure foundation there is developed 
what seems to me to be an argument so precarious that 
I dare not venture to present it except in the author's 
own words. 

These I shall give side by side with some critical queries 
to indicate where the argument seems to be faulty. After 
the enunciation of Henry's law we read : 

1 ' On the Transmission of Earthquake Waves through the Earth,' Pro- 
ceedings of Cambridge Philosophical Society, vol. xii, 1904. 



XII 



SEISMIC RADIATIONS 



235 



' Thus if rV be the volume 
of gas which can be held in 
solution by the volume V of 
the liquid, rV is the same 
for all pressures. It appar- 
ently follows that if the 
liquid be in a state of com- 
pression, so that when the 
pressure is relieved the 
volume V expands to V +v, 
the volume of gas which it 
can then hold in solution 
will be r(V +v). Conse- 
quently an additional volume 
of gas rv, proportional to the 
increase of volume of the 
liquid, can be held in solu- 
tion, and no gas will be 
extruded in consequence of 
the relief of pressure until 
the limit of expansibility of 
the liquid is reached, after 
which gas will be extruded 
as the pressure continues to 
fall.' 



Is there not some con- 
fusion here as to the precise 
interpretation of Henry's 
law ? The volumetric enun- 
ciation of the law is a mode 
of expression based on an 
experiment which takes no 
account of the negligibly 
slight volume changes of the 
liquid. Have we any war- 
rant to assume that in the 
initial stages of pressure re- 
lief the expansion of the 
liquid increases its absorp- 
tive power for a gas to such 
an extent as to overbalance 
the diminution in the mass 
of gas dissolved which, ac- 
cording to the exact state- 
ment of Henry's law, must 
accompany the diminution 
of the pressure ? Indeed, 
have we any warrant for the 
belief that the elastic expan- 
sion or contraction of a 
liquid has any measurable 
influence on its absorptive 
power for gases ? 



There then follows a mathematical investigation into 
the propagation of the complex disturbance here indicated, 
a disturbance consisting partly of elastic compression and 
partly of gas extrusion. The result gives a speed of pro- 
pagation whose square is Pe/(DP+Der), where D is the 
density of the fluid, e its incompressibility, P the pressure, 
and r as above. If there is no extrusion of gas this becomes 
the usual e/D. If the liquid were incompressible the dis- 
turbance would be transmitted because of the extruded gas 
with a speed equal to V(P/Dr). 



' These two effects cannot 
be simultaneous because . . . 
so long as the liquid expands 
no gas will be extruded. 

'Consider then the effect 



This paragraph reiterates 
the succession of changes 
criticized above, and em- 
phasizes the assumption that 
the magma must be satur- 



236 



EARTHQUAKE PHENOMENA 



XII 



of a diminution of pressure 
upon the magma at the 
origin of disturbance. The 
relaxation of pressure, al- 
though impulsive, cannot be 
instantaneous. The magma 
being under the compression 
corresponding to saturation, 
the relief of compression up 
to a certain point will in the 
first place cause voluminal 
expansion, which, as already 
shown, will not be accom- 
panied by extrusion of gas. 
This expansion will be pro- 
pagated as an elastic wave 
with the velocity Ve/D. As 
the relief of compression con- 
tinues, the expansion of the 
liquid magma will reach the 
limit of voluminal expansion 
and gas will begin to be 
extruded. This stage of the 
disturbance will be propa- 
gated as a second gaseous 
wave with a velocity VP/Dr 
less than that of the elastic 
wave with extrusion of gas 
but without further expan- 
sion of the liquid element of 
the magma . . . 

* Similar changes will occur 
at every place which the 
disturbance reaches during 
its passage. Thus the first 
effect will be voluminal ex- 
pansion, so that an elastic 
wave will be continually 
started in front of the gas- 
eous wave.' 

Assuming that this curious gaseous wave corresponds to 
the second preliminary tremors, Fisher proceeds to cal- 
culate the quantity r. The value comes out 0-0125, the 
density of the magma being taken at 2-68. Rise of temper- 
ature greatly reduces the power of liquids to absorb gases ; 



ated, the necessity for which 
on other grounds is not 
apparent. 

Still, admitting the deli- 
cate adjustment and the 
changes which are believed 
to occur, let us consider on 
its own merits the mode of 
propagation of the so-called 
gaseous wave. There is, of 
course, no difficulty about 
the other. 

A succession of pressure 
changes produces at a certain 
stage an extrusion of gas, 
and this phenomenon is pro- 
pagated through the magma. 
This implies not only that 
the whole magma is in its 
saturated state, but that the 
necessary pressure changes 
continue sufficiently ener- 
getic and sufficiently pro- 
longed to give rise to the 
extrusion at every point 
visited. But any tridimen- 
sional radiation of energy 
means a falling off in inten- 
sity as the disturbance 
reaches out to greater dis- 
tances. How under such 
circumstances are we to ima- 
gine the persistence of the 
conditions favourable for the 
extrusion of the gas ? 



XII SEISMIC RADIATIONS 237 

and at the high temperatures which exist in this case we 
should, reasoning from analogy, expect the absorption to be 
practically nil, unless the high pressures involved have an 
influence. But this would contradict Henry's law which is 
assumed throughout. It seems to me indeed that the theory 
advanced by Mr. Fisher is too ingenious ; but the author 
himself regards it as having served its purpose if it relieves 
the anxiety of those who hold by the internal fluidity of the 
earth. 

But may not the facts be more easily taken into account ? 
It will be granted by all that the physical condition of 
molten rock under the high pressures that certainly exist 
in the heart of the earth must be very different from what 
our surface experience associates with the term fluidity. 
For example, air at the temperature and pressure which 
exist at a depth of twenty miles will have a density com- 
parable with that of the rock. Whatever may be the 
results of individual experiments on the changes of volume 
when a substance solidifies or liquefies, the probability is 
that under great pressures and at high temperatures there 
is no clear line of division or demarcation between the two 
states. We know from experiment that elastic solids can 
be made to flow. During this process of yielding to the 
appropriate stress the material will still behave like an 
elastic solid to rapid variations of compressional and dis- 
tortional stresses and even of this very stress which is 
compelling it to flow. Fluidity and elasticity of form are not 
of necessity incompatible or mutually antagonistic. There 
is nothing physically unsound in the hypothesis that the 
nucleus of the earth is capable of transmitting distortional 
as well as compressional vibrations, but is at the same time 
incapable of resisting indefinitely continued action of steady 
distortional stresses. 

If, as is generally admitted, the two phases of the pre- 
liminary tremor be comparable with the compressional and 
distortional waves in an isotropic elastic solid, should we 
not expect to find some evidence that the vibrations are 
in the one case longitudinal, in the other transverse ? In 
other words, by careful comparison of the records of two 



238 EARTHQUAKE PHENOMENA XII 

seismometers set so as to record movements at right angles 
to each other, is it possible to detect a difference corre- 
sponding to the difference between longitudinal and trans- 
verse displacements? With this object in view Imamura l 
has studied the North-South and East-West records of 
various earthquakes as given by some of the Tokyo in- 
struments. No very clear conclusion can, however, be 
drawn. 

Omori, in his memoir on the Kangra quake, gives results 
agreeing fairly well with the hypothesis that the first and 
second preliminary phases are comparable with waves of 
longitudinal and transverse type. He considers that all 
the types of motion are transmitted along the arc ; but any 
probable brachistochronic path through the earth will satisfy 
the surface conditions quite as well. The Japan and Euro- 
pean stations are all situated relative to Kangra in such a 
position that the great circle drawn through each will pass 
very nearly east and west through the corresponding station. 
Hence we may assume that the East- West recording instru- 
ment will record mainly longitudinal displacements ; and the 
North-South transverse displacements. On the other hand, 
the American and Mexican stations are so situated that 
the great circles passing through them and the epicentre are 
approximately coincident with the meridian. Hence the 
North-South instrument will record mainly longitudinal 
vibrations and the East- West transverse. The general 
results are indicated in the following scheme, in which 
under each phase is given the azimuth of the instrument 
which gave the greater movement. Thus N means that 
the amplitude of the record of the corresponding phase was 
greater on the North-South instrument than on the East- 
West ; and the letter E means that the East-West record 
was the larger. The letters heading the columns refer to 
the different phases, P and S being the preliminary tremors, 
Lj, L 2 , L 3 being Omori's first, second, and third phases of 
the large waves (p. 200), and W the large waves along the 
major arc. 

1 Bulletin of the Imperial Earthquakes Investigation Committee, vol. i, 
No. 3, 1907. 



XII 



SEISMIC RADIATIONS 



PHASE AND DIRECTION OF MOTION 



239 



Region P S L, 


L 2 L 


w 


Tokyo . i 












Osaka . [EN 


N 


N E 


E 


Kobe. . t 


1 






Potsdam | 
Gottingen \ 


E 


N '. N 


N E 


E 


Quarto-Castello ) 












Leipzig . > 


E 


N N 


N N 





O'Gynalla \ 










Ischia 


E 


N 


N 


N E 





Tacubaya 
Cheltenham 


N i E 
unce 


E 

[tain 


E N 
X 


X 



Thus there is evidence that longitudinal displacements 
preponderate in the first preliminary phase and the third 
phase of the large waves, and the transverse displacements 
in the second phase and in earlier phases of the large 
waves. 

Rizzo has drawn similar conclusions from the records 
obtained in Europe of the Calabrian earthquake of Sep- 
tember 8, 1905. The four stations discussed are situated to 
the north of Calabria, so that we may regard north and 
south displacements as corresponding to the longitudinal 
vibration. 

PHASE AND DIRECTION OF MOTION 



Station 


P 


s ! 


Lipsia . . . 
Gottingen 
Upsala . . 
Tortosa . . 


N 
N 
N 
E 


K 
E 
E 

N 



Finally, Professor C. F. Marvin, who has charge of the 
Bosch- Omori seismometers at Washington, and who has 
improved the action of these instruments by some ingenious 
devices, 1 found a striking illustration of the same effect in 
the North-South and East-West records of the Kingston 
(Jamaica) earthquake of January 14, 1907. 2 Washington 
is only fifteen minutes of arc west of Kingston at a distance 
of 1400 miles, that is, almost due north ; and the East-West 
record showed no first phase of tremor. The following are 

1 Monthly Weather Review, May, 1906. 2 Ibid., January, 1907. 



240 EARTHQUAKE PHENOMENA XII 

the times of commencement of the different phases reckon- 
ing in minutes from an estimated epoch : 

PHASES AND DIRECTIONS OF MOTION 



* 


N-S 


E-W 


First Phase, Tremors . . \ 
Second ,, . . 
Beginning, Large Waves . 
End, . 


5-2 
9-7 
13-6 
21-9 


absent 
9-7 
13-5 
21-9 



The earlier advent of the large waves on the East-West 
record indicates predominant transverse vibrations in the 
early part of the principal portion. The same result is 
indicated in Omori's table given above. It has in my 
opinion a very significant bearing upon the mode of propa- 
gation of the large waves ; but this is more appropriately 
discussed further on. (See below, page 257.) 

The existence of three distinct types of earthquake 
radiations is now generally admitted, the most energetic 
part known as the large waves or principal portion being 
almost certainly transmitted through the comparatively 
thin heterogeneous layer which forms the so-called crust 
of the earth. The first and second phases of the preliminary 
tremors must be regarded as essentially elastic vibrations 
transmitted from the earthquake focus along brachisto- 
chronic paths to all parts of the earth's surface. My own 
opinion is that these paths are concave outward but nearly 
rectilinear in their deeper portions, so that in most cases 
they do not deviate far from lines of chords. 

As already stated, this view is not held by the Japanese 
seismologists. They favour an hypothesis which explains 
the times of advent of the preliminary tremors at distant 
stations in terms of assumed layers of quickest transmission. 
These layers are believed to lie parallel to the surface, so 
that the preliminary tremors travel arcually at a depth of 
perhaps sixty or one hundred miles. 

The hypothesis of a stratum of maximum velocity of 
transmission was first propounded by Nagaoka in his paper 
of 1900 on the Elastic Constants of Rocks (p. 162). We had 
long been familiar on seismological grounds with the idea 



XII SEISMIC RADIATIONS 241 

that the elastic modulus increased with depth, and Nagaoka's 
experiments on the elastic constants of rocks showed that 
this increase began to declare itself within the range of the 
accessible parts of the crust. In his general discussion of 
this question Nagaoka seems to me to take a curiously 
limited point of view. I quote the paragraph in which 
the hypothesis is broached. 

' As we go deep in the earth's crust the rocks generally 
assume schistose structure, we have reason to believe that 
the elastic constants of the constituent rocks increase in 
a certain particular direction, which evidently coincides 
with that of swiftest propagation of elastic disturbance. 
Pressed by the weight of the superincumbent crust these 
rocks will be of greater density, so that the increase of 
elastic constants is attended with corresponding increase of 
density. We cannot conceive that the elastic constant nor 
the density will continually increase as we approach the 
centre of the earth ; they will both attain asymptotic 
values. The alternatives are, either the ratio of elastic 
constants to density goes on gradually increasing, or it 
first reaches a maximum and then goes on decreasing. 
The former supposition makes the velocity of elastic waves 
increase from the surface towards the centre of the earth, 
while the latter implies the existence of the stratum of 
maximum velocity of propagation. Such a stratum, if it 
exists, will lie pretty deep in the earth's crust and will be 
inaccessible to us, but the question will be settled by the 
seismologists.' 

So far as I can discover, no real argument is advanced in 
favour of the hypothesis of the stratum of maximum velocity, 
which hypothesis is, however, taken for granted in the 
subsequent discussion. 

In the above paragraph there are several points which 
might be criticized; such, for example, as the assumption 
that the schistose character of our superficial rocks will be 
characteristic of the deeper parts of the crust where pre- 
sumably many earthquakes originate. As regards the main 
issue I am not aware of any reason which forbids us con- 
ceiving that both the density and the elastic moduli increase 
as we approach the centre of the earth. The probability 
is that both do increase, but that their ratio tends to an 
asymptotic value becoming practically constant long before 

KNOTT R 



242 EARTHQUAKE PHENOMENA XII 

the centre is reached. This most probable case is excluded 
from the so-called ' alternatives ', the second of which seems 
to me to be the least probable of all. 

In the preceding paragraphs the facts and theories of the 
new seismology have been presented mainly in their historic 
setting. It remains now to take as complete a view as 
possible of the whole problem. 

In the first place the evidence seems to me to be over- 
whelming in favour of the view that the preliminary tremors 
are not transmitted over the surface or even parallel to the 
surface, but pass by brachistochronic paths through the 
interior of the earth in accordance with the well-known laws 
of refraction of wave-motion. 

The large waves seem to be true surface waves in the 
sense that they are transmitted through the outer crust, 
so that the apparent speed of propagation along the surface 
is a true speed. 

If, however, the elastic waves which constitute the pre- 
liminary tremors are transmitted by brachistochronic paths 
through the body of the earth, emerging at various angles 
of incidence at the surface, then it is obvious from the first 
principles of wave- motion that the apparent speed of transit 
along the surface is not a real speed of propagation. It 
is the speed of the trace of the wave as it runs along the 
surface. Imagine the wave-front to be impinging internally 
on the earth's surface at an angle, say, of 30 with a speed 
of six kilometres per second. Then a simple geometrical 
construction shows that as the wave advances through 
ten kilometres, its trace on the surface advances through 
twenty. The angle which the wave-front makes with the 
surface is the complement of the angle between the surface 
and the direction of propagation ; and the ratio of the real 
speed of propagation to the apparent speed of transit of 
the trace along the surface is the cosine of this so-called 
angle of emergence. This relation lies at the root of the 
investigations into the reflexion and refraction of wave- 
motion at the boundary of two media as treated in the 
last chapter. It is used by Green in his paper on the re- 
flexion and refraction of light, and is no doubt as old as 



XII SEISMIC RADIATIONS 243 

Fresnel. 1 Nevertheless we find Dr. Benndorf in a paper on 
the transmission of earthquake waves (1906) demonstrating 
the theorem analytically and enunciating it as if it were 
altogether new in its generality. In a footnote he credits von 
Kovesligethy with proving it for a particular case in 1905. 

It is generally supposed that the first preliminary tremors 
correspond to the compressional waves (see chapters ix 
and x) transmitted through the body of the earth. On 
this hypothesis the vibrations are in the direction of pro- 
pagation, and will tend to cause a surface movement in the 
direction of the angle of emergence. The horizontal motion 
which is commonly measured will be only one component 
of the complete movement, and will be derived from it by 
multiplying by the cosine of the said angle. 

The first investigator who attempted to measure directly 
the angle of emergence of the preliminary tremors was 
Schliiter, 2 who deduced it from the measured vertical and 
horizontal displacements. The results are interesting, al- 
though we cannot ascribe to them any very great accuracy. 
For the sake of comparison with the theory to be given pre- 
sently, they are tabulated below, the first row being the 
arcual distance from the epicentre and the second the 
measured angle of emergence. 

ANGLES or EMERGENCE (SCHLUTEB) 

Arc in degrees . . 9 10 11 13 34 36 38 40 43 51 63 
Emergence-angle . 29 39 56 59 64 69 73 75 78 78 80 

Basing on these results Benndorf 3 shows that the time 
graph can be approximately reproduced by application of 
the relation connecting the apparent surface speed and the 
real speed at the surface, when that real speed is assumed to 
be 5-5 kilometres per second. 

The general fact established by Schliiter's results is that 
the angle of emergence increases with the arcual distance, a 

1 It is part and parcel of the elementary explanation of total reflexion 
according to the undulatory theory. 

1 Schwingungsart und Weg der Erdbebenwellen', Beitragezur Geophysik, 
vol. v, 1903. 

3 ' Fortpflanzung der Erdbebenwellen', Mitteilungen der Erdbeben-Kom- 
mission der Jcaiserl. Akad. der Wissensch. in Wien, No. 31, 1906. 

R2 



244 



EARTHQUAKE PHENOMENA 



XII 



fact in complete accordance with the view that the speed of 
propagation of the compressional wave increases with the 
depth. For arcual distances approaching 180 the angle of 
emergence will be so great that the cosine will be small and 
the horizontal component of the displacement correspond- 
ingly small and difficult to measure. This at once explains 
the frequently uncertain character of the first appearance of 
the tremors at great distances, and shows how important it 
is that the vertical component also should be measured. 
From a careful study of the comparative behaviour of various 
types of instrument Milne concluded, in 1903, that the ob- 
served times, as given in the table on page 229, should be 
considerably diminished ; and this view is supported by 
Benndorf in the paper already cited. From the evidence of 
the vertical motion Benndorf supplies corrections which agree 
fairly well with those given by Milne in 1903 ; and in the 
subsequent discussion we shall take these corrected values 
as the most satisfactory data at our disposal. They are 
given in the following table. 

CORRECTED TIMES OF TRANSIT OF PRELIMINARY TREMORS 
(MILNE AND BENNDORF) 



; Arc | First Phase Second Phase 



30 


5-2 min. ll-9min. 


60 


9-8 




17-5 




90 


13-1 




23-8 


9 


120 


15-3 




27-5 




150 


17 




30-5 





180 


18 




31-3 





Within the last ten years there have been many sugges- 
tions as to the paths pursued by seismic radiations through 
the earth. Some ten years earlier, however, in 1888, Schmidt 
drew forcible attention to the probability that the speed of 
propagation of earthquake disturbances in the neighbour- 
hood of the epicentre increased with depth below the surface. 
This implied that the paths of the seismic waves would 
necessarily be curved concave upward. Consequently the 
emergence angle of the shock at any locality could not be 
applied in the simple way at first imagined to the determina- 
tion of the position of the focus. When towards the end of 



XII SEISMIC RADIATIONS 245 

last century the transmission of seismic vibrations all over 
and through the earth came to be recognized, the problem of 
brachistochronic paths hitherto confined to optics had at 
once a geological and seismological bearing. As a piece of 
mathematics the problem may be thus stated : Given the 
law of change of speed of propagation with depth, find the 
form of the rays. 

In 1898, basing on Milne's earlier results, I drew a sketch 
of the probable forms of wave-fronts and paths of propaga- 
tion of compressional vibrations, which was published in the 
British Association Report for 1899. These curves were 
drawn by a tentative process in accordance with an assumed 
law connecting speed with depth ; for the material then to 
hand seemed too meagre to form the basis for a more formal 
attack. About the same time Rudzki published a paper 
in which the brachistochronic equations were worked out 
for a special integrable case, which did not, however, corre- 
spond with actuality. Somewhat earlier R. von Kovesli- 
gethy 1 had worked out the equations of radiation on the 
assumption that the speed of propagation diminished with 
the increase of depth. He was thus led to elliptic forms for 
the rays. In his second paper he shows how this can be 
made to harmonize with observation. Von Kovesligethy's 
mathematical work is admirable as the solution of a definite 
problem in wave propagation ; but there is certainly no 
physical basis for the implicit assumption that the speed of 
propagation of the elastic waves decreases as the depth in- 
creases, simply because the density is known to increase. 

Benndorf's paper already cited is undoubtedly the most 
important contribution to the subject made in recent years. 
Making certain plausible assumptions as to the limiting 
values of the quantities involved, he deduces synthetically 
a law of velocity change with depth, which satisfies the 
values of the angle of emergence as determined experimen- 
tally by Schliiter. It is clear, of course, that an accurate 
knowledge of the angles of emergence can give no exact in- 

1 'Neue Geometrische Theorie seismischer Erscheinungen ', Math. u. 
naturwissensch. JBerichte aus Ungarn, 1897. (The paper was presented 
in 1895. See also a later paper in the same publication for 1905. 



246 EARTHQUAKE PHENOMENA XII 

formation regarding the speed of propagation in the deeper 
parts of the earth ; and Benndorf 's solution is only one of 
many. The particular law of velocity change with depth 
to which he is led is indicated in the following table, in which 
x represents the distance from the centre in fractions of the 
earth's radius and v the speed in kilometres per second. 

x 0-0 0-2 0-4 0-6 0-8 0-9 0-95 0*975 1 
v 15-7 15-7 15-7 14-5 11-3 11-0 10-3 8-8 5-5 

As the distance from the centre increases the speed of 
propagation remains fairly constant up to nearly half the 
radius, then it diminishes with increase of distance, at first 
slowly, then more rapidly, then more slowly again, till 
about the distance x = O 95. From this distance to the sur- 
face the speed diminishes with great rapidity from 10-3 to 
5-5 kilometres per second. 

I propose now to consider the problem in a direct manner, 
with the view of discovering to what extent a fairly simple 
assumption of the law connecting depth and speed of propa- 
gation can be made to agree with the facts of observation, 
I shall state the assumptions and give the conclusions, re- 
ferring to a paper published in the Proceedings of the Royal 
Society of Edinburgh (1908) for the mathematical investi- 
gation. 

The problem can be treated with great simplicity as an 
example of Hamilton's general method of system of rays. 
Two cases are considered. In the first case the speed at 
depth x is represented by the formula v 2 = V' 2 ^x^ and 
the values V and /u are found so as to satisfy the surface 
value for v and the time of transmission across a diameter. 
After some trials I chose the expression 
v = 13-6 VT 2-a 2 

as satisfying fairly well the two conditions named. Starting 
from this expression we can work out with ease the forms of 
the wave-fronts and of the rays, the times taken to pass along 
these rays, the angles of emergence, and the final distribution 
of energy over the surface. In the following table the more 
important quantities are given along with the minimum 
radius vector (x) of the ray corresponding to the arc A, with 
reference to which the other quantities are tabulated. 



XII 



SEISMIC RADIATIONS 



247 



Case I. v = 13-6 Vl-2-x 2 throughout the globe. 



Arc A 


Transit 
Time 
T 


Minimum 
radius 

X 


Emergence Energy distribution 
angle ' over surface defined 
e by arc 


5 


1-6 


0-998 


10-3 3-26 


10-1 


2-9 


0-98 


26-6 20-04 


15-6 


4-3 


0-958 


36-4 35-26 


24-9 


6-5 


0-913 


47-9 54-99 


37-7 


8-8 


0-841 


57-6 71-24 


49-6 


10-6 


0-775 


63-4 80-03 


65 


12-4 


0-684 


69-0 87-22 


98-7 


14-9 


0-492 


73-4 95-02 


144-2 


17-5 


0-214 


84-9 99-21 


161-7 


17-8 


0-109 


87-4 99-82 


170-9 


17-9 


0-055 


88-7 99-97 


178-2 


18 


0-011 


89-8 99-99 


180 


18 





90 100 



Comparing the times of transit with the corrected times as 
given by Milne and Benndorf , we see that for arcs smaller 
than 100 the above table gives distinctly too high values. 
For arcs greater than 100 the values are in good agreement. 
This shows that the speed of propagation must alter more 
rapidly in the outer layers than is indicated in the formula 
assumed for v. 

This suggests the second case, in which the formula 

V 2 _. y-2 _ ^2 X 2 

is taken as holding from the surface to a depth of one-tenth 
of the radius, the speed remaining constant at all greater 
depths. After a few trials I chose the expression 

v = 24-45 \/l-06-z 2 

as holding true from x = 0- 9 to x = 1 . At the surface where 
x = 1 the speed is 6 kilometres per second ; and at all dis- 
tances from the centre up to x = 0-9 the speed is 12-23 kilo- 
metres per second. 

The ray will be wholly curved when it does not penetrate 
deeper than x = O 9 ; but when it penetrates deeper than 
this distance the middle portion will be straight. In the 
following table, when the arc and time are expressed by the 
sum of two numbers, the first refers to the curved beginning 
and end of the path, the second to the straight and middle 
portion. 



248 



EARTHQUAKE PHENOMENA 



XII 



Case II. v = 24-45 x/1-06 # 2 through the outer shell of 
one-tenth of the radius. 



Arc A 


Transit Time 
Tmin. 


Minimum 
radius 

X 


Emergence 
angle 
e 


Energy distribution 
over surface defined 
by arc 


1-7 


0-4 


0-999 


11-5 


8-03 


6 


2-0 


0-977 


42-4 


45-96 


17-9 


3-9 


0-922 


60-7 


76-1 


21-6 


4-5 


0-9 


63-8 


80-55 


14-2+ 38-5 


3-5+ 5-1 


0-85 


65-4 


82-65 


10-5+ 67-1 


3 + 8-6 


0-75 


68-4 


86-49 


6-7 + 111-4 


2-5 + 12-9 


0-50 


75-8 


94 


2-6+146-2 


2-4+15-3 


0-25 


83-0 


98-5 


180 


2-3 + 15-6 





90 


100 



The comparison of these two cases, with the actual case 
as represented by Milne's and Benndorf's corrections, is 
given in the following concise table derived graphically from 
the foregoing results, 





Time 


s of First P 


base 


Arc 


Case I 


Case II 


Milne and 
Benndorf 


30 
60 
90 
120 
150 
180 


7-5 
11-9 
14-5 
16-4 
17-6 
18 


5-7 
9-5 
13 
15-6 
17-6 
17-9 


5-2 
9-8 
13-1 

15-3 
17 

18 



The values for Case II are in very good agreement with 
those derived from observation. That is to say, the observed 
facts of seismic radiation can be co-ordinated on the assump- 
tion that throughout all but a comparatively thin crust of 
the earth the elastic waves of highest speed are transmitted 
with a speed of fully 12 kilometres per second, and that 
within this crust of thickness equal to one-tenth the radius 
the speed decreases from the value 12-23 at the inner surface 
to the value 6 at the outer surface. 

If this wave of highest speed be a compressible wave with 
longitudinal vibrations, the cosine of the angle of emergence 
of the ray will give the ratio of the magnitude of the hori- 
zontal motion to the whole amplitude. Now most of the 
observations have been obtained with instruments recording 



XII 



SEISMIC RADIATIONS 



249 



horizontal motion only, and comparatively few with instru- 
ments recording vertical motion. But at great arcual dis- 
tances from the epicentre the angle of emergence increases 
towards 90, with corresponding diminution in the value of 
the cosine, and the horizontal component of the displacement 
will be very small, ultimately vanishing at the antipodal 
point. At such great distances there will consequently be 
a tendency for the preliminary tremors (assumed to be 
mainly compressional) to be retarded in their arrival. As 
a matter of fact it is, as we have seen, extremely difficult at 
times to determine the exact moment at which the tremors 
begin on records which have been obtained at stations further 
distant than 100 from the epicentre. 

According to the theory here developed, we may obtain 
the times for the second phase of the preliminary tremors 
by increasing the times for the first phase in the ratio of 
31-3 to 18, assuming for the purpose Benndorf's corrected 
values. The results are as follows. 

TIMES OF TRANSIT OF SECOND PRELIMINARY TREMORS 



Arc 


Case I 


Case II 


Benndorf 


c=.8>8Vl-2-x~ 


< =14-05 -x/l-Oe-a;- 


30 


13 


9-9 


11-9 


60 


20-7 


16-5 


17-5 


90 


25-2 


22-6 


23-8 


120 


28-5 


27-1 


27-5 


150 


30-6 


30-6 


30-5 


180 


31-3 


31-1 


31-3 



This gives 3-45 kilometres per second for the surface 
speed, and 7-03 for the greatest speed in the interior. 

The agreement here is not quite so good as in the case of 
the first phase. It could be improved by slightly increasing 
the depth of the shell through which there is variation of 
speed of propagation. Viewed as a problem in elasticity 
this would mean that the modulus on which the speed of 
the second phase depended varied with depth according to 
a law not quite the same as that which held for the modulus 
determining the propagation of the first phase. The numbers 
for Case I are in somewhat closer agreement with observa- 
tion than the like numbers for the first phase. 



250 EARTHQUAKE PHENOMENA XII 

If the second phase be due to the arrival of the first tremors 
of the distortional wave, with displacements perpendicular 
to the direction of propagation, then the horizontal com- 
ponent of the displacement will be equal to the maximum 
displacement multiplied by the sine of the angle of emergence. 
Consequently, at great arcual distances, the second phase 
should tend to become proportionately in greater evidence 
than the first phase. There are, indeed, cases in which the 
second phase has been mistaken for the first, the latter having 
had too small a horizontal component to produce a record. 

It seems to me that the theory here sketched is amply 
sufficient to co-ordinate all the known phenomena. The first 
phase of the preliminary tremors is thus identified with the 
compressional waves passing through the body of the earth. 
No doubt, especially in the more heterogeneous crust, surfaces 
of discontinuity will in the manner explained in chapter x 
start waves of distortional type along with the incident 
waves of compressional type. But across the practically 
homogeneous nucleus the compressional waves will run ahead 
of their associates of other type, so that what emerges at 
the surface, although modified in detail, must be referable 
to these compressional waves. Similarly when, somewhat 
later, the distortional waves flow in in quantity, there will 
be mingled with them waves of the compressional type. 
Nevertheless the second phase will be mainly composed of 
disturbances which have passed through the homogeneous 
nucleus as distortional waves, but have emerged modified 
in detail by refraction across discontinuous surfaces. 

The distortional waves need not necessarily be more ener- 
getic than the compressional ; but their generally greater 
amplitude as measured on instruments recording horizontal 
motion is at once explained in terms of the angle of emer- 
gence. From the data on pages 247-8 we find that for 
arcual distances greater than 60 the sine of the angle of 
emergence is greater than the cosine in ratios exceeding the 
value 2, rapidly increasing for greater arcual distances. 

The longer periods which observation proves to be asso- 
ciated with the second phase do not seem to find an immediate 
explanation along the lines of this theory. But may these 



XII SEISMIC RADIATIONS 251 

not be explained as due to the intermingling of the quicker 
distortional vibrations with the less rapid compressional 
vibrations, which, because of their longer period, have 
travelled slower than the compressional waves of quicker 
vibration ? True, the mathematical theory of elasticity does 
not recognize any relation between speed of propagation 
and length of wave ; but this theory is only a first approxi- 
mation to reality, and proves nothing either one way or the 
other as to what may occur in seismic vibrations. The fact 
that the first phase when well developed always begins with 
comparatively rapid oscillations seems indeed to establish the 
truth that shorter waves do travel faster than longer waves. 
If we take four seconds to be the shortest period we find that 
the disturbance travelling with a speed of 12-23 kilometres 
per second will have a wave-length of nearly 49 kilometres. 

It may be of some interest to compare the elastic constants 
of the material of the nucleus of the earth on the assumption 
that we are dealing with compressional and distortional 
waves. The ratio of the speeds of the two types is 31-3 to 
16 or 1-74 to unity. The ratio of the wave-moduli will be as 
the square of this or almost exactly 3 to 1. Hence in the 
notation of chapters ix and x we have 

k + 4^/3 =3n 

where k is the incompressibility and n the rigidity. This 
gives 3k = 5n 

a noteworthy result, showing that the inner parts of the 
earth almost accurately fulfil the conditions of isotropy pos- 
sessed by the ideal elastic solid of Navier and Poisson. This 
conclusion seems to me to be an additional argument in 
favour of the view now being presented. 

Here in the heart of the earth is a material at a high 
temperature and under great pressure, brought into a physi- 
cal state suggesting homogeneity, though not necessarily 
implying it. As shown long ago by Tait, this globe is 
held together mainly by gravitational attraction. The 
cohesion between the molecules is, however, the force which 
is involved in the propagation of the elastic disturbances 
which radiate from a seismic centre. The view of the 
French elasticians was that true homogeneity required 



252 



EARTHQUAKE PHENOMENA 



XII 



a definite relation between incompressibility and rigidity. 
This definite relation is not realized in the case of materials 
tested by ordinary combinations of stress and strain. This 
fact, however, was not admitted by de St. Venant as dis- 
proving the uniconstant theory developed by Navier and 
Poisson ; for as soon as an aeolotropic stress is applied to our 
rods and wires, the material ceases to be truly isotropic. 




Ed 
CASE I 



CASE IE 



FIG. 43. 



It would appear from the calculation just made that the 
interior of the earth is in a condition which at each point 
might be described as isotropic; and the relation required 
by the uniconstant theory is accurately satisfied by the con- 
stants calculated from the propagation of the two phases 
of the preliminary tremors when these are assumed to be 
respectively the compressional and distortional vibrations. 
We shall now consider the significance of the last column 



XII 



SEISMIC RADIATIONS 



253 



of figures in the tables on pages 247 and 248, the columns 
headed Energy Distribution. The meaning of the figures is 
best explained by consideration of particular cases in con- 
nexion with the foregoing diagram. 

The diagram represents a section of the globe, and some 
of the particulars corresponding to each of the cases are 
figured on the one half. The full lines show the paths 
of the seismic disturbances as they radiate out from the 
origin 0. Each ray corresponds to one of the particular set 
of values tabulated on pages 247, 248. The following short 
table gives the value of the arc corresponding to each ray, the 
rays being represented by the terminal letter on the diagram : 



Ray 


A 


B 


C 


D 


E 


Case I . 
Case II . . 


24-9 
21-6 


49-6 
52-7 


65-0 
77-6 


98-7 
118-1 


144-2 

148-8 



To each full line OA, OB, OC, &c., there corresponds 
a dotted line Oa, Ob, Oc, &c., which starts tangential to 
the curved ray and is therefore the direction in which 
the disturbance begins to radiate outwards from the origin. 
Considerations of symmetry show at once that the angle 
which each dotted line makes with the surface at the origin 
is the same as the angle with which the ray emerges at 
the other end. In other words, this angle is equal to the 
emergence angle as tabulated above. 

In the diagram the left-hand semicircle shows the rays 
for the first case, in which the variation of speed is assumed 
to take place throughout the whole globe ; and the right- 
hand diagram the second case, in which the variation takes 
place only through the upper layer of thickness equal to 
one-tenth of the radius. In the latter case the first ray OA 
lies wholly within the layer of varying speed of propagation, 
and is curved throughout its whole length. All the other 
rays represented pass partly through the interior of constant 
speed of propagation and are straight throughout a part 
of their course. Thus the rays OD, OE to distant points are 
very approximately coincident with chords, but for shorter 
rays such as OC and OB the chordal coincidence is not 
so close. We shall discuss this case in some detail. 



254 EARTHQUAKE PHENOMENA XII 

The dotted line Oa in Case II gives the direction in which 
a ray would have passed if the speed of propagation had 
been absolutely constant throughout the whole globe. This 
condition would have given rise to what we may call the 
spherical distribution of energy over the surface of the globe, 
half the energy being in fact distributed over the hemisphere 
of which the origin is the pole. But in the case represented 
in the right-hand semicircle the ray starting originally 
along the dotted line Oa becomes bent round by refraction 
so as to assume the position OA. The energy, of course, 
passes with it. Hence the energy which in the simple case 
of spherical distribution would have been distributed over 
the part of the surface defined by the arc Oa with as pole 
is concentrated within the much smaller part of the surface 
defined by the arc OA. We are to imagine Oa to be one of 
a cone of rays which divides the spherical surface into two 
parts, defined respectively by the arcs into which Oa divides 
the semicircle. The semivertical angle of this cone is equal 
to 90 e, where e is the corresponding angle of emergence 
belonging to the ray OA ; and the area on the spherical 
surface defined by the arc Oa is proportional to 

1+cos (180-2e)=l-cos 2e. 

This number, divided by 2, the value when e = 90, represents 
the fraction of the energy which is finally distributed over 
the surface defined by the arc OA. Thus in the particular 
case which has been the subject of discussion, 80-1 per cent, 
of the whole energy is found distributed over the com- 
paratively small fraction of the surface whose boundary 
lies 21- 6 from the epicentre. In spherical distribution 
only 3-5 per cent, of the whole energy would have appeared 
over this surface. Glancing back to the table for Case II, 
we see that 50 per cent, of the whole energy is distributed 
over the small surface whose boundary lies about 7 from 
the epicentre, and that 75 per cent, is distributed over the 
surface which does not extend to 18 from the epicentre. 
In spherical distribution these surfaces would have received 
respectively only J and 2J per cent, of the whole energy. 

It is interesting to compare the two cases figured side by 
side on the diagram, and to notice how much more con- 



XII SEISMIC EADIATIONS 255 

centrated the energy is in the neighbourhood of the epicentre 
in Case II, which is characterized by a rapid variation of 
speed of propagation within the upper layers of the earth. 

In these calculations I have, for simplicity, assumed the 
origin to be at the surface. This is never quite the case 
in large, world-shaking earthquakes. These originate at 
depths which may vary from 10 to 50 miles. Nevertheless, 
because of the curving of the seismic rays the energy 
will be distributed unequably in a manner similar to 
what is here indicated. The deeper the origin the less 
unequable will the final distribution be ; but so long as 
the origin lies within the layer of changing velocity, there 
must be the curving round of the seismic rays, carrying their 
energy with them. 

Let there be two earthquakes of equal intensity but with 
their origins at different depths. The one with the shallow 
focus will have its energy strongly concentrated towards the 
surface regions immediately in the vicinity of the epicentre ; 
while the energy associated with the deeper focus will be less 
unequably distributed over the whole surface. The latter 
will be registered all the world over as a world-shaking earth- 
quake, while the former may appear much more limited in 
its sphere of action, simply because of the small intensity of 
the tremors which pass to distant regions. 

It would be possible, though somewhat laborious, to work 
out the surface distribution of energy for several depths of 
origin along the lines indicated above. If this were done, 
and if instruments could be constructed to give an accurate 
measure of the energy associated with seismic movements 
at the surface, we should be in possession of a method for 
determining the depths of origins a problem which has 
hitherto baffled all endeavours. 

In the case of earthquakes, various complications of wave- 
motion will come in to alter the character of the vibrations. 
For example, if, as is highly probable, the speed of propaga- 
tion depends on the wave-length, there will be interference 
of wave-motions of nearly equal wave-length to produce the 
phenomenon of group- velocities. The speed with which the 
group advances will be greater or less than the speed of 



256 EARTHQUAKE PHENOMENA XII 

propagation of the individual waves, according as this latter 
speed diminishes or increases with increase of wave-length. 
In all probability the speed of the purely elastic waves which 
run ahead of the earthquake disturbance is independent of 
the wave-length ; but the evidence of the records seems to 
suggest that what we have called the quasi-elastic waves 
travel more slowly as the wave-lengths increase. Hence in 
such cases wave groups will advance through the waves at 
a somewhat greater speed. The existence of wave groups 
will have its own effect upon the character of the records 
producing appearances analogous to those of resonance. 
Also it is conceivable that the long wave-lengths present 
in the record may really be the intervals between groups of 
waves and not a true original wave-length in the ground. 

Another kind of complication may arise from effects of 
dispersion. Nagaoka has considered this question in an 
interesting manner, and has found evidence in the seismo- 
grams of a phenomenon analogous to what is known as 
anomalous dispersion in optics. 

It is sufficient to draw attention to some of the compli- 
cated accompaniments of waves in heterogeneous media in 
order to guard ourselves against basing conclusions upon a 
too simple and therefore incomplete theory of wave-motion. 
One great fact established by these seismological observa- 
tions is that vibrational disturbances can be propagated 
throughout the whole body of the earth. They must be 
regarded as elastic ; and the fact of their propagation proves 
that in the deeper parts of the earth viscosity is of small 
account. Another fact of importance is the recognition of 
three distinct types of vibratory motion, the two kinds of 
preliminary tremors and the large waves. 

I have several times expressed the view that the large 
waves are transmitted by a succession of reflexions within 
the crust from the upper surface which is backed by air or 
water. The result obtained both by Omori and Marvin 
(p. 239) as to the preponderance of transverse vibrations in 
the early phases of this portion of the earthquake record is 
of no little interest when looked at in the light of the 
theory of elastic waves as developed in chapter x. I refer 



XII SEISMIC RADIATIONS 257 

especially to the conclusions arrived at in connexion with 
reflexion and refraction of elastic waves at a boundary of 
rock and water or rock and air (pp. 175 to 181). In both 
these cases, for high incidences in the neighbourhood of 80, 
the energy incident in the condensational type of wave is 
very largely transformed by reflexion into the distortional 
or transverse type, whereas the incident distortional waves 
are themselves largely reflected as distortional still. Thus 
whatever be the original type of the incident wave, succes- 
sive reflexions at the high incidences necessarily imply an 
increasing proportion of transverse vibrations. Marvin's 
clear-cut result described above on page 239 is at once 
explained along the lines of the theory here advocated. The 
first phase of tremors passed directly from Kingston to 
Washington by concave paths through rock only, largely 
preserving their longitudinal character, and failing to pro- 
duce a record on the EW. instrument. The second phase 
marked the influx of transverse vibrations superposed upon 
the longitudinal vibrations, and thus both instruments 
responded. The early portions of the large waves, which 
quite possibly began as longitudinal motion through the 
shallow parts of the crust, became by reflexion at the water- 
backed surface of the earth's crust so largely impregnated 
with transverse vibrations as to indicate their presence on the 
EW. instrument a few seconds earlier than on the NS. in- 
strument. It is not to be expected, of course, that all the phe- 
nomena can be brought into line with the purely elastic theory. 
But there is a mental satisfaction in finding some point of re- 
semblance between this theory and the results of observation. 

The general problem of seismic vibrations set up in the 
earth is one of great complexity ; for even the compara- 
tively simple case of the vibrations of a homogeneous 
elastic sphere the size of our globe presents great difficulties. 
The fundamental modes of vibration of an elastic sphere 
were investigated in 1882 by Professor Horace Lamb in a 
paper which has become classical. 1 According to his results 
all modes of vibration can be grouped under two types, the 
one of which corresponds to the purely distortional type 
1 Proceedings of London Mathematical Society, vol. xiii. 

KNOTT S 



258 EARTHQUAKE PHENOMENA XII 

referred to above. The other does not, however, correspond 
to the simple dilatational type, but involves rotational strain. 
The frequencies of the higher modes of vibration approxi- 
mate in each case to the series of natural numbers 5, 6, 7, 8, 
&c. ; but the series in the two types are not necessarily 
commensurable. Lamb shows that the slowest mode of 
vibration of a steel sphere the size of the earth would have 
a period of seventy-eight minutes. The higher modes will 
have higher frequencies, the period of the 21st mode being, 
for example, about one minute, of the 42nd half a minute, 
and so on. Now we have seen that periods may range from 
three or four seconds to nearly a minute. There is thus no 
difficulty in accounting for the presence of a number of 
different periods in earth tremors. The difficulty is rather 
to explain why the periods are so limited in number. 

In the elastic sphere imagined by Lamb, a condensation 
produced at any locality will be resisted by the incompressi- 
bility of the material, and will start a series of condensational 
rarefactional waves. But if we suppose the sphere to be 
under its own gravitational action any alteration of density 
will, so far as gravitational effect is concerned, tend to be 
accentuated. Material will tend to move towards the denser 
region and away from the less dense. In other words, gravi- 
tation implies an instability which must be resisted by the 
elastic properties of the material. This consideratio